%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL130-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art07.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 : Sun Nov 28 00:09:04 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/SystemOnTPTP25758/LCL/LCL130-1+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 = 1 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 52] [nf = 0] [nu = 26] [ut = 17] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 119] [nf = 5] [nu = 62] [ut = 17] % 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(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v8 dv4 f7 c0 t15 td6 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) % U4: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))))) % U9: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) % U38: < d4 v6 dv3 f13 c8 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) % U50: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(equivalent_2(x0,x4),x5))) % U53: < d4 v4 dv2 f3 c0 t7 td3 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1 % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))))) ....... U4 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2)))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U38: % ~is_a_theorem_1(equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_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(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_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(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))))) ....... R2 [R1:L1, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1), equivalent_2(x0, equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))))) ....... R3 [R2:L1, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2)))), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))) ....... R4 [R3:L1, U9:L0] % Derivation of unit clause U50: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), equivalent_2(x0, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U9:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), x5), equivalent_2(equivalent_2(x0, x4), x5))) ....... R4 [R3:L0, U9:L0] % Derivation of unit clause U53: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), equivalent_2(x0, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U9:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(equivalent_2(x0,x4),x5))) ....... U50 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x1))) ....... R4 [R3:L0, U50:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) ....... U53 % ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) ....... U38 % [] ....... R1 [U53:L0, U38:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 297 % resolvents: 288 factors: 9 % Number of unit clauses generated: 209 % % unit clauses generated to total clauses generated: 70.37 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 15 [4] = 37 % Total = 54 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 209 [2] = 77 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)9 (-)45 % ------------------ % Total: (+)9 (-)45 % Total number of unit clauses retained: 54 % Number of clauses skipped because of their length: 31 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 313 % Number of unification failures: 136 % Number of unit to unit unification failures: 395 % 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: 79 % 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: 1436 % Total number of terms of all unit clauses in table: 2326 % 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: 0.62 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 449 % ConstructUnitClause() = 131 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.36 secs % %------------------------------------------------------------------------------