%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP004-2 : 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 : Sat Nov 27 20:39:32 EST 2010 % Result : Unsatisfiable 0.23s % Output : Refutation 0.23s % 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/SystemOnTPTP8101/GRP/GRP004-2+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 = 10] [nf = 0] [nu = 0] [ut = 4] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 146] [nf = 32] [nu = 62] [ut = 27] % Looking for a proof at depth = 3 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~product_3(a_0(),inverse_1(a_0()),identity_0()) % B1: product_3(x0,x1,multiply_2(x0,x1)) % B2: product_3(identity_0(),x0,x0) % B3: product_3(inverse_1(x0),x0,identity_0()) % B4: ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) % B5: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) % B6: ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) % B7: ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) % Unit Clauses: % -------------- % U1: < d0 v4 dv2 f1 c0 t5 td2 b > product_3(x0,x1,multiply_2(x0,x1)) % U2: < d0 v2 dv1 f0 c1 t3 td1 b > product_3(identity_0(),x0,x0) % U3: < d0 v2 dv1 f1 c1 t4 td2 b > product_3(inverse_1(x0),x0,identity_0()) % U4: < d2 v0 dv0 f2 c3 t5 td3 > ~equalish_2(multiply_2(a_0(),inverse_1(a_0())),identity_0()) % U7: < d2 v2 dv1 f2 c1 t5 td3 > equalish_2(identity_0(),multiply_2(inverse_1(x0),x0)) % U8: < d2 v2 dv1 f1 c1 t4 td2 > equalish_2(multiply_2(identity_0(),x0),x0) % U12: < d2 v2 dv1 f2 c2 t6 td3 > product_3(identity_0(),identity_0(),multiply_2(inverse_1(x0),x0)) % U13: < d2 v2 dv1 f1 c2 t5 td2 > product_3(identity_0(),multiply_2(identity_0(),x0),x0) % U22: < d2 v2 dv1 f3 c2 t7 td3 > ~product_3(inverse_1(x0),x0,multiply_2(a_0(),inverse_1(a_0()))) % U78: < d3 v4 dv2 f2 c0 t6 td3 > product_3(multiply_2(inverse_1(x0),x0),x1,x1) % U175: < d3 v2 dv1 f4 c2 t8 td3 > ~product_3(inverse_1(inverse_1(a_0())),multiply_2(inverse_1(x0),x0),a_0()) % U197: < d3 v4 dv2 f2 c0 t6 td2 > product_3(inverse_1(x0),multiply_2(x0,x1),x1) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % product_3(x0,x1,multiply_2(x0,x1)) ....... U1 % Derivation of unit clause U2: % product_3(identity_0(),x0,x0) ....... U2 % Derivation of unit clause U3: % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % Derivation of unit clause U4: % ~product_3(a_0(),inverse_1(a_0()),identity_0()) ....... B0 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B4 % ~equalish_2(x0, identity_0()) | ~product_3(a_0(), inverse_1(a_0()), x0) ....... R1 [B0:L0, B4:L2] % product_3(x0,x1,multiply_2(x0,x1)) ....... U1 % ~equalish_2(multiply_2(a_0(), inverse_1(a_0())), identity_0()) ....... R2 [R1:L1, U1:L0] % Derivation of unit clause U7: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B5 % ~product_3(x0, x1, x2) | equalish_2(x2, multiply_2(x0, x1)) ....... R1 [B1:L0, B5:L0] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % equalish_2(identity_0(), multiply_2(inverse_1(x0), x0)) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U8: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B5 % ~product_3(x0, x1, x2) | equalish_2(multiply_2(x0, x1), x2) ....... R1 [B1:L0, B5:L1] % product_3(identity_0(),x0,x0) ....... U2 % equalish_2(multiply_2(identity_0(), x0), x0) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U12: % product_3(identity_0(),x0,x0) ....... B2 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B4 % ~equalish_2(x0, x1) | product_3(identity_0(), x0, x1) ....... R1 [B2:L0, B4:L1] % equalish_2(identity_0(),multiply_2(inverse_1(x0),x0)) ....... U7 % product_3(identity_0(), identity_0(), multiply_2(inverse_1(x0), x0)) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U13: % product_3(identity_0(),x0,x0) ....... B2 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B4 % ~equalish_2(x0, x1) | product_3(identity_0(), x0, x1) ....... R1 [B2:L0, B4:L1] % equalish_2(multiply_2(identity_0(),x0),x0) ....... U8 % product_3(identity_0(), multiply_2(identity_0(), x0), x0) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U22: % product_3(inverse_1(x0),x0,identity_0()) ....... B3 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B5 % ~product_3(inverse_1(x0), x0, x1) | equalish_2(x1, identity_0()) ....... R1 [B3:L0, B5:L0] % ~equalish_2(multiply_2(a_0(),inverse_1(a_0())),identity_0()) ....... U4 % ~product_3(inverse_1(x0), x0, multiply_2(a_0(), inverse_1(a_0()))) ....... R2 [R1:L1, U4:L0] % Derivation of unit clause U78: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) ....... B6 % ~product_3(x0, multiply_2(x1, x2), x3) | ~product_3(x0, x1, x4) | product_3(x4, x2, x3) ....... R1 [B1:L0, B6:L1] % product_3(identity_0(),multiply_2(identity_0(),x0),x0) ....... U13 % ~product_3(identity_0(), identity_0(), x0) | product_3(x0, x1, x1) ....... R2 [R1:L0, U13:L0] % product_3(identity_0(),identity_0(),multiply_2(inverse_1(x0),x0)) ....... U12 % product_3(multiply_2(inverse_1(x0), x0), x1, x1) ....... R3 [R2:L0, U12:L0] % Derivation of unit clause U175: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x3, x2, multiply_2(x4, x1)) ....... R1 [B1:L0, B7:L0] % product_3(multiply_2(inverse_1(x0),x0),x1,x1) ....... U78 % ~product_3(x0, multiply_2(inverse_1(x1), x1), x2) | product_3(x0, x3, multiply_2(x2, x3)) ....... R2 [R1:L0, U78:L0] % ~product_3(inverse_1(x0),x0,multiply_2(a_0(),inverse_1(a_0()))) ....... U22 % ~product_3(inverse_1(inverse_1(a_0())), multiply_2(inverse_1(x0), x0), a_0()) ....... R3 [R2:L1, U22:L0] % Derivation of unit clause U197: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x2,x3,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x0,x4,x5) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B7:L1] % product_3(identity_0(),x0,x0) ....... U2 % ~product_3(x0, x1, identity_0()) | product_3(x0, multiply_2(x1, x2), x2) ....... R2 [R1:L0, U2:L0] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % product_3(inverse_1(x0), multiply_2(x0, x1), x1) ....... R3 [R2:L0, U3:L0] % Derivation of the empty clause: % product_3(inverse_1(x0),multiply_2(x0,x1),x1) ....... U197 % ~product_3(inverse_1(inverse_1(a_0())),multiply_2(inverse_1(x0),x0),a_0()) ....... U175 % [] ....... R1 [U197:L0, U175:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 30720 % resolvents: 30666 factors: 54 % Number of unit clauses generated: 29930 % % unit clauses generated to total clauses generated: 97.43 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 4 [2] = 23 [3] = 171 % Total = 198 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 29930 [2] = 753 [3] = 37 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] equalish_2 (+)12 (-)1 % [1] product_3 (+)103 (-)82 % ------------------ % Total: (+)115 (-)83 % Total number of unit clauses retained: 198 % Number of clauses skipped because of their length: 1346 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 30741 % Number of unification failures: 52655 % Number of unit to unit unification failures: 8446 % N literal unification failure due to lookup root_id table: 72 % N base clause resolution failure due to lookup table: 5 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 11 % N unit clauses dropped because they exceeded max values: 29679 % N unit clauses dropped because too much nesting: 6783 % 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: 8 % Max term depth in a unit clause: 4 % Number of states in UCFA table: 610 % Total number of terms of all unit clauses in table: 1395 % Max allowed number of states in UCFA: 80000 % Ratio n states used/total allowed states: 0.01 % Ratio n states used/total unit clauses terms: 0.44 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 83396 % ConstructUnitClause() = 29873 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.01 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.23 secs % %------------------------------------------------------------------------------