%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : COL109-2 : TPTP v5.0.0. Released v3.2.0. % 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 : Sat Nov 27 18:01:28 EST 2010 % Result : Unsatisfiable 0.87s % Output : Refutation 0.87s % 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/SystemOnTPTP26827/COL/COL109-2+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 = 7] [nf = 0] [nu = 1] [ut = 5] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 82129] [nf = 2] [nu = 52282] [ut = 14917] % Looking for a proof at depth = 3 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: c_in_3(c_Pair_4(v_z_0(),v_w_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % B3: ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(),v_x_H_0()),v_y_Ha_0()),v_w_0()),x0,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0())),x0,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % B5: ~c_in_3(c_Pair_4(x2,x3,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(x0,x1,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x2,x0),c_Comb_Ocomb_Oop_A_D_D_2(x3,x1),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % Unit Clauses: % -------------- % U1: < d0 v0 dv0 f2 c7 t9 td2 b nc > c_in_3(c_Pair_4(v_xb_0(),v_x_H_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % U2: < d0 v0 dv0 f2 c7 t9 td2 b nc > c_in_3(c_Pair_4(v_yb_0(),v_y_Ha_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % U3: < d0 v7 dv3 f8 c6 t21 td5 b > c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(),x0),x1),x2),c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(x0,x2),c_Comb_Ocomb_Oop_A_D_D_2(x1,x2)),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % U38: < d2 v0 dv0 f4 c9 t13 td3 > c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_x_H_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % U39: < d2 v0 dv0 f4 c9 t13 td3 > c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % U14917: < d3 v0 dv0 f4 c9 t13 td3 > ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % c_in_3(c_Pair_4(v_xb_0(),v_x_H_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U1 % Derivation of unit clause U2: % c_in_3(c_Pair_4(v_yb_0(),v_y_Ha_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U2 % Derivation of unit clause U3: % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(),x0),x1),x2),c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(x0,x2),c_Comb_Ocomb_Oop_A_D_D_2(x1,x2)),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U3 % Derivation of unit clause U38: % c_in_3(c_Pair_4(v_z_0(),v_w_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B0 % ~c_in_3(c_Pair_4(x2,x3,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(x0,x1,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x2,x0),c_Comb_Ocomb_Oop_A_D_D_2(x3,x1),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B5 % ~c_in_3(c_Pair_4(x0, x1, tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x0, v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(x1, v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R1 [B0:L0, B5:L1] % c_in_3(c_Pair_4(v_xb_0(),v_x_H_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U1 % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(), v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(v_x_H_0(), v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U39: % c_in_3(c_Pair_4(v_z_0(),v_w_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B0 % ~c_in_3(c_Pair_4(x2,x3,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(x0,x1,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x2,x0),c_Comb_Ocomb_Oop_A_D_D_2(x3,x1),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B5 % ~c_in_3(c_Pair_4(x0, x1, tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x0, v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(x1, v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R1 [B0:L0, B5:L1] % c_in_3(c_Pair_4(v_yb_0(),v_y_Ha_0(),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U2 % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(), v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(), v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U14917: % ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(),v_x_H_0()),v_y_Ha_0()),v_w_0()),x0,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0())),x0,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B3 % ~c_in_3(c_Pair_4(x2,x3,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(x0,x1,tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) | c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(x2,x0),c_Comb_Ocomb_Oop_A_D_D_2(x3,x1),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... B5 % ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(), v_x_H_0()), v_y_Ha_0()), v_w_0()), c_Comb_Ocomb_Oop_A_D_D_2(x0, x1), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(), v_z_0()), x0, tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(), v_z_0()), x1, tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R1 [B3:L1, B5:L2] % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_OS_0(),x0),x1),x2),c_Comb_Ocomb_Oop_A_D_D_2(c_Comb_Ocomb_Oop_A_D_D_2(x0,x2),c_Comb_Ocomb_Oop_A_D_D_2(x1,x2)),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U3 % ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(), v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(v_x_H_0(), v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) | ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(), v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(), v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R2 [R1:L0, U3:L0] % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_xb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_x_H_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U38 % ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(), v_z_0()), c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(), v_w_0()), tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0()), c_Comb_Oparcontract_0(), tc_prod_2(tc_Comb_Ocomb_0(), tc_Comb_Ocomb_0())) ....... R3 [R2:L0, U38:L0] % Derivation of the empty clause: % ~c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U14917 % c_in_3(c_Pair_4(c_Comb_Ocomb_Oop_A_D_D_2(v_yb_0(),v_z_0()),c_Comb_Ocomb_Oop_A_D_D_2(v_y_Ha_0(),v_w_0()),tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0()),c_Comb_Oparcontract_0(),tc_prod_2(tc_Comb_Ocomb_0(),tc_Comb_Ocomb_0())) ....... U39 % [] ....... R1 [U14917:L0, U39:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 171680 % resolvents: 171654 factors: 26 % Number of unit clauses generated: 141780 % % unit clauses generated to total clauses generated: 82.58 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 4 [1] = 1 [2] = 14912 [3] = 1 % Total = 14918 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 141780 [2] = 29878 [3] = 22 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] c_in_3 (+)14916 (-)2 % ------------------ % Total: (+)14916 (-)2 % Total number of unit clauses retained: 14918 % Number of clauses skipped because of their length: 29 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 171687 % Number of unification failures: 93062 % Number of unit to unit unification failures: 14954 % N literal unification failure due to lookup root_id table: 101 % N base clause resolution failure due to lookup table: 13 % N UC-BCL resolution dropped due to lookup table: 9013 % Max entries in substitution set: 8 % N unit clauses dropped because they exceeded max values: 37368 % N unit clauses dropped because too much nesting: 20127 % 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: 61 % Max term depth in a unit clause: 11 % Number of states in UCFA table: 389906 % Total number of terms of all unit clauses in table: 609258 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.74 % Ratio n states used/total unit clauses terms: 0.64 % Number of symbols (columns) in UCFA: 47 % Profile 2: Number of calls to: % ============================== % PTUnify() = 264749 % ConstructUnitClause() = 52282 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.17 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.86 secs % %------------------------------------------------------------------------------