%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL083-2 : TPTP v5.0.0. Bugfixed v1.2.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art03.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 23:54:33 EST 2010 % Result : Unsatisfiable 1.43s % Output : Refutation 1.43s % 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/SystemOnTPTP23855/LCL/LCL083-2+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 ... % t = 0 secs [nr = 291] [nf = 0] [nu = 177] [ut = 82] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 715] [nf = 5] [nu = 478] [ut = 82] % 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(implies_2(implies_2(a_0(),b_0()),a_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)))) % B3: ~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: < d0 v2 dv1 f1 c0 t3 td2 b > is_a_theorem_1(implies_2(x0,x0)) % U11: < d2 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) % U13: < d2 v7 dv4 f6 c0 t13 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x1,x2)))) % U15: < d2 v8 dv5 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x1)),implies_2(x4,implies_2(x3,x1)))) % U236: < d4 v10 dv3 f13 c4 t27 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))) % U1139: < d4 v19 dv8 f22 c4 t45 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),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(implies_2(x5,x6),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))))) % U2475: < d4 v26 dv12 f29 c4 t59 td8 > ~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(implies_2(x4,x5),implies_2(x6,x5)),implies_2(x5,x7)),implies_2(x8,implies_2(x5,x7))),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))))) % U4865: < d4 v9 dv5 f8 c0 t17 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x1),implies_2(x0,x1)),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(x0,x0)) ....... U2 % Derivation of unit clause U11: % 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) ....... B3 % ~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, B3:L1] % is_a_theorem_1(implies_2(x0,x0)) ....... U2 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U13: % 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) ....... B3 % ~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, B3:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) ....... U11 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(x1, x2)))) ....... R2 [R1:L0, U11:L0] % Derivation of unit clause U15: % 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) ....... B3 % ~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, B3:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x1,x2)))) ....... U13 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x3, x1)), implies_2(x4, implies_2(x3, x1)))) ....... R2 [R1:L0, U13:L0] % Derivation of unit clause U236: % ~is_a_theorem_1(implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))) ....... R1 [B0:L0, B3:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R2 [R1:L1, B3:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R3 [R2:L0, R2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) ....... U11 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R4 [R3:L0, U11:L0] % Derivation of unit clause U1139: % 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) ....... B3 % ~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, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~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, B3: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),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))) ....... U236 % ~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), x5), implies_2(x7, x5)), implies_2(implies_2(implies_2(implies_2(x5, x6), x5), implies_2(x7, x5)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))))) ....... R4 [R3:L1, U236:L0] % Derivation of unit clause U2475: % 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) ....... B3 % ~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, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~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, B3:L0] % is_a_theorem_1(implies_2(x0,x0)) ....... 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))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2:L0] % ~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),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(implies_2(x5,x6),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))))) ....... U1139 % ~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(implies_2(x4, x5), implies_2(x6, x5)), implies_2(x5, x7)), implies_2(x8, implies_2(x5, x7))), implies_2(implies_2(implies_2(implies_2(x9, x10), x9), implies_2(x11, x9)), implies_2(implies_2(implies_2(implies_2(x9, x10), x9), implies_2(x11, x9)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))))) ....... R4 [R3:L1, U1139:L0] % Derivation of unit clause U4865: % 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) ....... B3 % ~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, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~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, B3:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x1)),implies_2(x4,implies_2(x3,x1)))) ....... U15 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x2), implies_2(x1, x2))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15: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(implies_2(x0, x1), x2), x1), implies_2(x0, x1)), 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(implies_2(x0,x1),x2),x1),implies_2(x0,x1)),x3),implies_2(x4,x3))) ....... U4865 % ~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(implies_2(x4,x5),implies_2(x6,x5)),implies_2(x5,x7)),implies_2(x8,implies_2(x5,x7))),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))))) ....... U2475 % [] ....... R1 [U4865:L0, U2475:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 9180 % resolvents: 9171 factors: 9 % Number of unit clauses generated: 8799 % % unit clauses generated to total clauses generated: 95.85 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 79 [4] = 4784 % Total = 4866 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 8799 [2] = 364 [3] = 17 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)114 (-)4752 % ------------------ % Total: (+)114 (-)4752 % Total number of unit clauses retained: 4866 % Number of clauses skipped because of their length: 152 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 9202 % Number of unification failures: 11491 % Number of unit to unit unification failures: 539374 % N literal unification failure due to lookup root_id table: 35 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 11 % Max entries in substitution set: 19 % N unit clauses dropped because they exceeded max values: 2941 % N unit clauses dropped because too much nesting: 224 % 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: 58934 % Total number of terms of all unit clauses in table: 230368 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.11 % Ratio n states used/total unit clauses terms: 0.26 % Number of symbols (columns) in UCFA: 38 % Profile 2: Number of calls to: % ============================== % PTUnify() = 20693 % ConstructUnitClause() = 7804 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.04 secs % -------------------------------------------------------- % | | % Inferences per sec: 9180 % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 1.42 secs % %------------------------------------------------------------------------------