%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL080-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art05.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 23:50:28 EST 2010 % Result : Unsatisfiable 1.14s % Output : Refutation 1.14s % 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/SystemOnTPTP27697/LCL/LCL080-1+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 = 7] [nf = 0] [nu = 0] [ut = 4] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 3713] [nf = 0] [nu = 2428] [ut = 1019] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 10848] [nf = 8] [nu = 8265] [ut = 1019] % 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()),c_0()),implies_2(implies_2(c_0(),a_0()),implies_2(e_0(),a_0())))) % B1: is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) % B2: is_a_theorem_1(implies_2(x0,implies_2(x1,x0))) % B3: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),x0)) % B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v6 dv3 f5 c0 t11 td4 b > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) % U3: < d0 v4 dv2 f3 c0 t7 td4 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),x0)) % U9: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3))) % U11: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x3),implies_2(implies_2(x1,x2),x3)))) % U12: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x0,x4)),x2),x3))) % U13: < d2 v10 dv5 f9 c0 t19 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x3,x4),implies_2(implies_2(x2,x0),x4)))) % U14: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4))) % U33: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x0),x1))) % U40: < d2 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),x2),x3),implies_2(implies_2(x0,x2),x3))) % U92: < d2 v7 dv4 f6 c0 t13 td6 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x2,implies_2(implies_2(implies_2(x0,x3),x0),x1)))) % U110: < d2 v6 dv4 f5 c0 t11 td5 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1)))) % U443: < d2 v6 dv2 f5 c0 t11 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(implies_2(x0,x1),x1))) % U2142: < d4 v10 dv6 f16 c7 t33 td7 > ~is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1))),implies_2(implies_2(implies_2(implies_2(implies_2(a_0(),b_0()),x4),x5),implies_2(implies_2(c_0(),x4),x5)),implies_2(implies_2(c_0(),a_0()),implies_2(e_0(),a_0()))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... U1 % Derivation of unit clause U3: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),x0)) ....... U3 % Derivation of unit clause U9: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... U1 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x2, x0), x3))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U11: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3))) ....... U9 % is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(implies_2(implies_2(x0, x2), x3), implies_2(implies_2(x1, x2), x3)))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U12: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x3),implies_2(implies_2(x1,x2),x3)))) ....... U11 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), implies_2(implies_2(implies_2(implies_2(x1, x4), implies_2(x0, x4)), x2), x3))) ....... R2 [R1:L0, U11:L0] % Derivation of unit clause U13: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x0,x4)),x2),x3))) ....... U12 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x3, x4), implies_2(implies_2(x2, x0), x4)))) ....... R2 [R1:L0, U12:L0] % Derivation of unit clause U14: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x1, x2), implies_2(x0, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x3,x4),implies_2(implies_2(x2,x0),x4)))) ....... U13 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x3, x1), x2)), x4), implies_2(implies_2(x0, x3), x4))) ....... R2 [R1:L0, U13:L0] % Derivation of unit clause U33: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(x0, x1)) | is_a_theorem_1(implies_2(implies_2(x1, x2), implies_2(x0, x2))) ....... R1 [B1:L0, B4:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),x0)) ....... U3 % is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(implies_2(implies_2(x0, x2), x0), x1))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U40: % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(x1,x2),implies_2(x0,x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(x0, x1)) | is_a_theorem_1(implies_2(implies_2(x1, x2), implies_2(x0, x2))) ....... R1 [B1:L0, B4:L1] % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(implies_2(implies_2(x0,x2),x0),x1))) ....... U33 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), x2), x3), implies_2(implies_2(x0, x2), x3))) ....... R2 [R1:L0, U33:L0] % Derivation of unit clause U92: % is_a_theorem_1(implies_2(x0,implies_2(x1,x0))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, x0)), x2)) | is_a_theorem_1(x2) ....... R1 [B2:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),x2),x3),implies_2(implies_2(x0,x2),x3))) ....... U40 % is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, implies_2(implies_2(implies_2(x0, x3), x0), x1)))) ....... R2 [R1:L0, U40:L0] % Derivation of unit clause U110: % is_a_theorem_1(implies_2(x0,implies_2(x1,x0))) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, x0)), x2)) | is_a_theorem_1(x2) ....... R1 [B2:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x2,implies_2(implies_2(implies_2(x0,x3),x0),x1)))) ....... U92 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), implies_2(x3, x1)))) ....... R2 [R1:L0, U92:L0] % Derivation of unit clause U443: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),x0)) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), x0), x2)) | is_a_theorem_1(x2) ....... R1 [B3:L0, B4:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4))) ....... U14 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(implies_2(x0, x1), x1))) ....... R2 [R1:L0, U14:L0] % Derivation of unit clause U2142: % ~is_a_theorem_1(implies_2(implies_2(implies_2(a_0(),b_0()),c_0()),implies_2(implies_2(c_0(),a_0()),implies_2(e_0(),a_0())))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), c_0()), implies_2(implies_2(c_0(), a_0()), implies_2(e_0(), a_0()))))) ....... R1 [B0:L0, B4:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B4 % ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), c_0()), implies_2(implies_2(c_0(), a_0()), implies_2(e_0(), a_0()))))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, x0)) ....... R2 [R1:L0, B4:L2] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x3,x1),x2)),x4),implies_2(implies_2(x0,x3),x4))) ....... U14 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(a_0(), b_0()), x1), x2), implies_2(implies_2(c_0(), x1), x2)), implies_2(implies_2(c_0(), a_0()), implies_2(e_0(), a_0()))))) ....... R3 [R2:L0, U14:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1)))) ....... U110 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), implies_2(x3, x1))), implies_2(implies_2(implies_2(implies_2(implies_2(a_0(), b_0()), x4), x5), implies_2(implies_2(c_0(), x4), x5)), implies_2(implies_2(c_0(), a_0()), implies_2(e_0(), a_0()))))) ....... R4 [R3:L0, U110:L0] % Derivation of the empty clause: % ~is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1))),implies_2(implies_2(implies_2(implies_2(implies_2(a_0(),b_0()),x4),x5),implies_2(implies_2(c_0(),x4),x5)),implies_2(implies_2(c_0(),a_0()),implies_2(e_0(),a_0()))))) ....... U2142 % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(implies_2(x0,x1),x1))) ....... U443 % [] ....... R1 [U2142:L0, U443:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 12637 % resolvents: 12627 factors: 10 % Number of unit clauses generated: 10038 % % unit clauses generated to total clauses generated: 79.43 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 4 [2] = 1015 [4] = 1124 % Total = 2143 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 10038 [2] = 2578 [3] = 21 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)312 (-)1831 % ------------------ % Total: (+)312 (-)1831 % Total number of unit clauses retained: 2143 % Number of clauses skipped because of their length: 32 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 12661 % Number of unification failures: 3316 % Number of unit to unit unification failures: 571231 % N literal unification failure due to lookup root_id table: 43 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 64 % Max entries in substitution set: 13 % N unit clauses dropped because they exceeded max values: 1708 % N unit clauses dropped because too much nesting: 682 % 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: 28574 % Total number of terms of all unit clauses in table: 78475 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.05 % Ratio n states used/total unit clauses terms: 0.36 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 15977 % ConstructUnitClause() = 3847 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.01 secs % -------------------------------------------------------- % | | % Inferences per sec: 12637 % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 1.13 secs % %------------------------------------------------------------------------------