%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : SET011-1 : 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 04:47:08 EST 2010 % Result : Unsatisfiable 3.04s % Output : Refutation 3.04s % 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/SystemOnTPTP1722/SET/SET011-1+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 = 7] [nf = 0] [nu = 0] [ut = 3] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 74] [nf = 17] [nu = 3] [ut = 5] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 585] [nf = 137] [nu = 32] [ut = 5] % Looking for a proof at depth = 4 ... % t = 1 secs [nr = 3427] [nf = 550] [nu = 315] [ut = 11] % Looking for a proof at depth = 5 ... % t = 1 secs [nr = 18381] [nf = 3089] [nu = 1453] [ut = 11] % Looking for a proof at depth = 6 ... % t = 3 secs [nr = 775257] [nf = 80729] [nu = 124010] [ut = 144] % Looking for a proof at depth = 7 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~intersection_3(a_0(),b_0(),aD_aDb_0()) % B1: difference_3(a_0(),b_0(),aDb_0()) % B2: difference_3(a_0(),aDb_0(),aD_aDb_0()) % B5: member_2(member_of_1_not_of_2_2(x0,x1),x0) | subset_2(x0,x1) % B6: ~member_2(member_of_1_not_of_2_2(x0,x1),x1) | subset_2(x0,x1) % B12: member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x0) | intersection_3(x0,x1,x2) % B13: member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x1) | intersection_3(x0,x1,x2) % B16: ~subset_2(x1,x0) | ~subset_2(x0,x1) | equal_sets_2(x1,x0) % B18: ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2) % B19: ~member_2(h_3(x0,x1,x2),x0) | ~member_2(h_3(x0,x1,x2),x1) | ~member_2(h_3(x0,x1,x2),x2) | intersection_3(x0,x1,x2) % Unit Clauses: % -------------- % U1: < d0 v0 dv0 f0 c3 t3 td1 b > difference_3(a_0(),b_0(),aDb_0()) % U2: < d0 v0 dv0 f0 c3 t3 td1 b > difference_3(a_0(),aDb_0(),aD_aDb_0()) % U3: < d2 v2 dv1 f0 c0 t2 td1 > subset_2(x0,x0) % U4: < d2 v2 dv1 f0 c0 t2 td1 > equal_sets_2(x0,x0) % U5: < d4 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) % U12: < d6 v0 dv0 f1 c4 t5 td2 > ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0()) % U34: < d6 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),b_0()) % U70: < d6 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),aD_aDb_0()) % U193: < d7 v0 dv0 f0 c2 t2 td1 > ~subset_2(b_0(),b_0()) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % difference_3(a_0(),b_0(),aDb_0()) ....... U1 % Derivation of unit clause U2: % difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2 % Derivation of unit clause U3: % member_2(member_of_1_not_of_2_2(x0,x1),x0) | subset_2(x0,x1) ....... B5 % ~member_2(member_of_1_not_of_2_2(x0,x1),x1) | subset_2(x0,x1) ....... B6 % subset_2(x0, x0) | subset_2(x0, x0) ....... R1 [B5:L0, B6:L0] % subset_2(x0, x0) ....... R2 [R1:L0, R1:L1] % Derivation of unit clause U4: % ~subset_2(x1,x0) | ~subset_2(x0,x1) | equal_sets_2(x1,x0) ....... B16 % ~subset_2(x0, x0) | equal_sets_2(x0, x0) ....... R1 [B16:L0, B16:L1] % subset_2(x0,x0) ....... U3 % equal_sets_2(x0, x0) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U5: % ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0 % member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x0) | intersection_3(x0,x1,x2) ....... B12 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R1 [B0:L0, B12:L2] % ~member_2(x3,x2) | ~difference_3(x0,x1,x2) | member_2(x3,x0) ....... B8 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) | ~difference_3(x0, x1, aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R2 [R1:L0, B8:L0] % ~difference_3(a_0(), x0, aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R3 [R2:L0, R2:L2] % difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R4 [R3:L0, U2:L0] % Derivation of unit clause U12: % ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0 % member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x1) | intersection_3(x0,x1,x2) ....... B13 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R1 [B0:L0, B13:L2] % ~member_2(x0,x2) | ~member_2(x0,x1) | ~difference_3(x3,x1,x2) ....... B7 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~difference_3(x1, x0, aD_aDb_0()) ....... R2 [R1:L0, B7:L0] % difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R3 [R2:L2, U2:L0] % ~member_2(x0,x2) | ~member_2(x0,x1) | ~difference_3(x3,x1,x2) ....... B7 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~difference_3(x1, b_0(), x0) ....... R4 [R3:L0, B7:L1] % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~difference_3(x0, b_0(), aDb_0()) ....... R5 [R4:L0, R4:L1] % difference_3(a_0(),b_0(),aDb_0()) ....... U1 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R6 [R5:L1, U1:L0] % Derivation of unit clause U34: % difference_3(a_0(),b_0(),aDb_0()) ....... B1 % ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2) ....... B18 % ~member_2(x0, a_0()) | member_2(x0, aDb_0()) | member_2(x0, b_0()) ....... R1 [B1:L0, B18:L1] % member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R2 [R1:L0, U5:L0] % ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R3 [R2:L0, B11:L0] % ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0()) ....... U12 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(aDb_0(), aDb_0()) ....... R4 [R3:L2, U12:L0] % ~equal_sets_2(x0,x1) | subset_2(x0,x1) ....... B3 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~equal_sets_2(aDb_0(), aDb_0()) ....... R5 [R4:L1, B3:L1] % equal_sets_2(x0,x0) ....... U4 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R6 [R5:L1, U4:L0] % Derivation of unit clause U70: % difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... B2 % ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2) ....... B18 % ~member_2(x0, a_0()) | member_2(x0, aD_aDb_0()) | member_2(x0, aDb_0()) ....... R1 [B2:L0, B18:L1] % member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R2 [R1:L0, U5:L0] % ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~subset_2(aD_aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R3 [R2:L0, B11:L0] % ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0()) ....... U12 % ~subset_2(aD_aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R4 [R3:L0, U12:L0] % ~equal_sets_2(x0,x1) | subset_2(x0,x1) ....... B3 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~equal_sets_2(aD_aDb_0(), x0) ....... R5 [R4:L0, B3:L1] % equal_sets_2(x0,x0) ....... U4 % member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R6 [R5:L1, U4:L0] % Derivation of unit clause U193: % ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0 % ~member_2(h_3(x0,x1,x2),x0) | ~member_2(h_3(x0,x1,x2),x1) | ~member_2(h_3(x0,x1,x2),x2) | intersection_3(x0,x1,x2) ....... B19 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R1 [B0:L0, B19:L3] % member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R2 [R1:L0, U5:L0] % ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~subset_2(x0, b_0()) ....... R3 [R2:L0, B11:L2] % member_2(h_3(a_0(),b_0(),aD_aDb_0()),aD_aDb_0()) ....... U70 % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~subset_2(x0, b_0()) ....... R4 [R3:L0, U70:L0] % ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11 % ~subset_2(x0, b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x1) | ~subset_2(x1, x0) ....... R5 [R4:L0, B11:L2] % ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(b_0(), b_0()) ....... R6 [R5:L0, R5:L2] % member_2(h_3(a_0(),b_0(),aD_aDb_0()),b_0()) ....... U34 % ~subset_2(b_0(), b_0()) ....... R7 [R6:L0, U34:L0] % Derivation of the empty clause: % ~subset_2(b_0(),b_0()) ....... U193 % subset_2(x0,x0) ....... U3 % [] ....... R1 [U193:L0, U3:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 876844 % resolvents: 792655 factors: 84189 % Number of unit clauses generated: 124538 % % unit clauses generated to total clauses generated: 14.20 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 2 [4] = 6 [6] = 133 [7] = 50 % Total = 194 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 124538 [2] = 393786 [3] = 358520 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] equal_sets_2 (+)1 (-)6 % [1] member_2 (+)67 (-)21 % [2] subset_2 (+)4 (-)6 % [3] difference_3 (+)2 (-)40 % [4] intersection_3 (+)0 (-)47 % ------------------ % Total: (+)74 (-)120 % Total number of unit clauses retained: 194 % Number of clauses skipped because of their length: 2032957 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 17319 % Number of successful unifications: 876877 % Number of unification failures: 6650478 % Number of unit to unit unification failures: 1513 % N literal unification failure due to lookup root_id table: 3547225 % N base clause resolution failure due to lookup table: 1359533 % N UC-BCL resolution dropped due to lookup table: 10856 % Max entries in substitution set: 15 % N unit clauses dropped because they exceeded max values: 101628 % 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: 5 % Max term depth in a unit clause: 2 % Number of states in UCFA table: 230 % Total number of terms of all unit clauses in table: 732 % Max allowed number of states in UCFA: 80000 % Ratio n states used/total allowed states: 0.00 % Ratio n states used/total unit clauses terms: 0.31 % Number of symbols (columns) in UCFA: 46 % Profile 2: Number of calls to: % ============================== % PTUnify() = 7527355 % ConstructUnitClause() = 101819 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.10 secs % -------------------------------------------------------- % | | % Inferences per sec: 292281 % | | % -------------------------------------------------------- % Elapsed time: 3 secs % CPU time: 3.04 secs % %------------------------------------------------------------------------------