%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL101-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art02.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 00:00:05 EST 2010 % Result : Unsatisfiable 1.20s % Output : Refutation 1.20s % 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/SystemOnTPTP1434/LCL/LCL101-1+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 = 5] [nf = 0] [nu = 0] [ut = 3] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 167] [nf = 0] [nu = 95] [ut = 47] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 408] [nf = 7] [nu = 255] [ut = 47] % 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(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) % B1: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) % B2: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) % B3: ~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(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) % U2: < d0 v8 dv4 f7 c0 t15 td6 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) % U7: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)))) % U33: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) % U103: < d4 v2 dv1 f9 c8 t19 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x0,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) % U104: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x3,x4)),equivalent_2(equivalent_2(x5,x0),equivalent_2(x5,x1))))) % U170: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),equivalent_2(x2,x1))))) % U574: < d4 v16 dv8 f23 c8 t47 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),equivalent_2(x5,x6)),x3)),equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x7,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... U1 % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... U2 % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),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) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... U2 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U33: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U103: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R1 [B0:L0, B3:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, B3:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)))) ....... U7 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6))), equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R3 [R2:L1, U7:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... U2 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x0, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R4 [R3:L1, U2:L0] % Derivation of unit clause U104: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),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) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), 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, B3:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6)), x3))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x3, x4)), equivalent_2(equivalent_2(x5, x0), equivalent_2(x5, x1))))) ....... R4 [R3:L0, U33:L0] % Derivation of unit clause U170: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),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) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), 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, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x3,x4)),equivalent_2(equivalent_2(x5,x0),equivalent_2(x5,x1))))) ....... U104 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7)), equivalent_2(x6, x7)), x4)))), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U104:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), equivalent_2(x2, x1))))) ....... R4 [R3:L0, U33:L0] % Derivation of unit clause U574: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),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) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x2)), x0))) ....... R2 [R1:L0, B3:L2] % ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x0,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U103 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x3, x4)), x1)), equivalent_2(equivalent_2(x5, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x5, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R3 [R2:L0, U103:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6)), x3)), equivalent_2(equivalent_2(x7, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x7, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R4 [R3:L0, U33:L0] % Derivation of the empty clause: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),equivalent_2(x5,x6)),x3)),equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x7,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) ....... U574 % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),equivalent_2(x2,x1))))) ....... U170 % [] ....... R1 [U574:L0, U170:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 89576 % resolvents: 89565 factors: 11 % Number of unit clauses generated: 88361 % % unit clauses generated to total clauses generated: 98.64 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 44 [4] = 528 % Total = 575 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 88361 [2] = 1196 [3] = 19 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)89 (-)486 % ------------------ % Total: (+)89 (-)486 % Total number of unit clauses retained: 575 % Number of clauses skipped because of their length: 1066 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 89596 % Number of unification failures: 109103 % Number of unit to unit unification failures: 43187 % N literal unification failure due to lookup root_id table: 36 % 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: 19 % N unit clauses dropped because they exceeded max values: 87520 % 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: 11 % Number of states in UCFA table: 11839 % Total number of terms of all unit clauses in table: 30973 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.02 % Ratio n states used/total unit clauses terms: 0.38 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 198699 % ConstructUnitClause() = 88092 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.42 secs % -------------------------------------------------------- % | | % Inferences per sec: 89576 % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 1.19 secs % %------------------------------------------------------------------------------