%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : GRP047-2 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art05.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 20:45:21 EST 2010 % Result : Unsatisfiable 0.33s % Output : Refutation 0.33s % 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/SystemOnTPTP4848/GRP/GRP047-2+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 = 11] [nf = 0] [nu = 0] [ut = 5] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 188] [nf = 28] [nu = 91] [ut = 37] % Looking for a proof at depth = 3 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~equalish_2(multiply_2(c_0(),a_0()),multiply_2(c_0(),b_0())) % B1: product_3(x0,x1,multiply_2(x0,x1)) % B2: product_3(identity_0(),x0,x0) % B5: ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) % B6: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) % B7: ~product_3(x0,x4,x5) | ~product_3(x1,x3,x4) | ~product_3(x0,x1,x2) | product_3(x2,x3,x5) % B8: ~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: < d0 v0 dv0 f0 c2 t2 td1 b > equalish_2(a_0(),b_0()) % U6: < d2 v0 dv0 f2 c5 t7 td2 > ~product_3(identity_0(),multiply_2(c_0(),b_0()),multiply_2(c_0(),a_0())) % U10: < d2 v0 dv0 f3 c5 t8 td3 > ~equalish_2(multiply_2(identity_0(),multiply_2(c_0(),b_0())),multiply_2(c_0(),a_0())) % U15: < d2 v0 dv0 f2 c5 t7 td3 > ~product_3(c_0(),a_0(),multiply_2(identity_0(),multiply_2(c_0(),b_0()))) % U17: < d2 v2 dv1 f1 c1 t4 td2 > equalish_2(multiply_2(identity_0(),x0),x0) % U19: < d2 v0 dv0 f0 c3 t3 td1 > product_3(identity_0(),a_0(),b_0()) % U23: < d2 v2 dv1 f1 c2 t5 td2 > product_3(identity_0(),multiply_2(identity_0(),x0),x0) % U47: < d3 v4 dv2 f3 c1 t8 td3 > product_3(multiply_2(x0,inverse_1(x1)),x1,multiply_2(x0,identity_0())) % U48: < d3 v2 dv1 f3 c2 t7 td4 > product_3(identity_0(),x0,multiply_2(inverse_1(inverse_1(x0)),identity_0())) % U74: < d3 v0 dv0 f2 c5 t7 td2 > ~product_3(multiply_2(identity_0(),c_0()),a_0(),multiply_2(c_0(),b_0())) % U76: < d3 v0 dv0 f1 c4 t5 td2 > ~product_3(c_0(),identity_0(),multiply_2(identity_0(),c_0())) % U116: < d3 v0 dv0 f2 c5 t7 td2 > ~product_3(identity_0(),multiply_2(c_0(),identity_0()),multiply_2(identity_0(),c_0())) % U129: < d3 v2 dv1 f2 c2 t6 td3 > product_3(multiply_2(inverse_1(x0),identity_0()),x0,identity_0()) % U199: < d3 v0 dv0 f2 c4 t6 td3 > ~product_3(identity_0(),multiply_2(c_0(),inverse_1(c_0())),identity_0()) % U348: < d3 v2 dv1 f2 c2 t6 td3 > product_3(identity_0(),multiply_2(x0,inverse_1(x0)),identity_0()) % --------------- 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: % equalish_2(a_0(),b_0()) ....... U4 % Derivation of unit clause U6: % ~equalish_2(multiply_2(c_0(),a_0()),multiply_2(c_0(),b_0())) ....... B0 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B6 % ~product_3(x0, x1, multiply_2(c_0(), b_0())) | ~product_3(x0, x1, multiply_2(c_0(), a_0())) ....... R1 [B0:L0, B6:L2] % product_3(identity_0(),x0,x0) ....... U2 % ~product_3(identity_0(), multiply_2(c_0(), b_0()), multiply_2(c_0(), a_0())) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U10: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B5 % ~equalish_2(multiply_2(x0, x1), x2) | product_3(x0, x1, x2) ....... R1 [B1:L0, B5:L1] % ~product_3(identity_0(),multiply_2(c_0(),b_0()),multiply_2(c_0(),a_0())) ....... U6 % ~equalish_2(multiply_2(identity_0(), multiply_2(c_0(), b_0())), multiply_2(c_0(), a_0())) ....... R2 [R1:L1, U6:L0] % Derivation of unit clause U15: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B6 % ~product_3(x0, x1, x2) | equalish_2(x2, multiply_2(x0, x1)) ....... R1 [B1:L0, B6:L0] % ~equalish_2(multiply_2(identity_0(),multiply_2(c_0(),b_0())),multiply_2(c_0(),a_0())) ....... U10 % ~product_3(c_0(), a_0(), multiply_2(identity_0(), multiply_2(c_0(), b_0()))) ....... R2 [R1:L1, U10:L0] % Derivation of unit clause U17: % product_3(x0,x1,multiply_2(x0,x1)) ....... B1 % ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B6 % ~product_3(x0, x1, x2) | equalish_2(multiply_2(x0, x1), x2) ....... R1 [B1:L0, B6: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 U19: % product_3(identity_0(),x0,x0) ....... B2 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B5 % ~equalish_2(x0, x1) | product_3(identity_0(), x0, x1) ....... R1 [B2:L0, B5:L1] % equalish_2(a_0(),b_0()) ....... U4 % product_3(identity_0(), a_0(), b_0()) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U23: % product_3(identity_0(),x0,x0) ....... B2 % ~equalish_2(x0,x1) | ~product_3(x2,x3,x0) | product_3(x2,x3,x1) ....... B5 % ~equalish_2(x0, x1) | product_3(identity_0(), x0, x1) ....... R1 [B2:L0, B5:L1] % equalish_2(multiply_2(identity_0(),x0),x0) ....... U17 % product_3(identity_0(), multiply_2(identity_0(), x0), x0) ....... R2 [R1:L0, U17:L0] % Derivation of unit clause U47: % 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) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B7:L0] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % ~product_3(x0, inverse_1(x1), x2) | product_3(x2, x1, multiply_2(x0, identity_0())) ....... R2 [R1:L0, U3:L0] % product_3(x0,x1,multiply_2(x0,x1)) ....... U1 % product_3(multiply_2(x0, inverse_1(x1)), x1, multiply_2(x0, identity_0())) ....... R3 [R2:L0, U1:L0] % Derivation of unit clause U48: % 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) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B7:L0] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % ~product_3(x0, inverse_1(x1), x2) | product_3(x2, x1, multiply_2(x0, identity_0())) ....... R2 [R1:L0, U3:L0] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % product_3(identity_0(), x0, multiply_2(inverse_1(inverse_1(x0)), identity_0())) ....... R3 [R2:L0, U3:L0] % Derivation of unit clause U74: % 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) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B7:L0] % product_3(identity_0(),multiply_2(identity_0(),x0),x0) ....... U23 % ~product_3(multiply_2(identity_0(), x0), x1, x2) | product_3(x0, x1, multiply_2(identity_0(), x2)) ....... R2 [R1:L1, U23:L0] % ~product_3(c_0(),a_0(),multiply_2(identity_0(),multiply_2(c_0(),b_0()))) ....... U15 % ~product_3(multiply_2(identity_0(), c_0()), a_0(), multiply_2(c_0(), b_0())) ....... R3 [R2:L1, U15:L0] % Derivation of unit clause U76: % 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) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x4, x1, multiply_2(x3, x2)) ....... R1 [B1:L0, B7:L0] % ~product_3(multiply_2(identity_0(),c_0()),a_0(),multiply_2(c_0(),b_0())) ....... U74 % ~product_3(x0, a_0(), b_0()) | ~product_3(c_0(), x0, multiply_2(identity_0(), c_0())) ....... R2 [R1:L2, U74:L0] % product_3(identity_0(),a_0(),b_0()) ....... U19 % ~product_3(c_0(), identity_0(), multiply_2(identity_0(), c_0())) ....... R3 [R2:L0, U19:L0] % Derivation of unit clause U116: % 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) ....... B7 % ~product_3(x0, multiply_2(x1, x2), x3) | ~product_3(x0, x1, x4) | product_3(x4, x2, x3) ....... R1 [B1:L0, B7:L1] % product_3(identity_0(),x0,x0) ....... U2 % ~product_3(identity_0(), multiply_2(x0, x1), x2) | product_3(x0, x1, x2) ....... R2 [R1:L1, U2:L0] % ~product_3(c_0(),identity_0(),multiply_2(identity_0(),c_0())) ....... U76 % ~product_3(identity_0(), multiply_2(c_0(), identity_0()), multiply_2(identity_0(), c_0())) ....... R3 [R2:L1, U76:L0] % Derivation of unit clause U129: % 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) ....... B7 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x1) | product_3(multiply_2(x0, x3), x4, x2) ....... R1 [B1:L0, B7:L2] % product_3(inverse_1(x0),x0,identity_0()) ....... U3 % ~product_3(x0, x1, x2) | product_3(multiply_2(inverse_1(x2), x0), x1, identity_0()) ....... R2 [R1:L0, U3:L0] % product_3(identity_0(),x0,x0) ....... U2 % product_3(multiply_2(inverse_1(x0), identity_0()), x0, identity_0()) ....... R3 [R2:L0, U2:L0] % Derivation of unit clause U199: % 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) ....... B8 % ~product_3(x0, x1, x2) | ~product_3(x3, x0, x4) | product_3(x3, x2, multiply_2(x4, x1)) ....... R1 [B1:L0, B8:L0] % product_3(multiply_2(x0,inverse_1(x1)),x1,multiply_2(x0,identity_0())) ....... U47 % ~product_3(x0, multiply_2(x1, inverse_1(x2)), x3) | product_3(x0, multiply_2(x1, identity_0()), multiply_2(x3, x2)) ....... R2 [R1:L0, U47:L0] % ~product_3(identity_0(),multiply_2(c_0(),identity_0()),multiply_2(identity_0(),c_0())) ....... U116 % ~product_3(identity_0(), multiply_2(c_0(), inverse_1(c_0())), identity_0()) ....... R3 [R2:L1, U116:L0] % Derivation of unit clause U348: % 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) ....... B8 % ~product_3(x0, x1, x2) | ~product_3(x3, x4, x0) | product_3(x3, multiply_2(x4, x1), x2) ....... R1 [B1:L0, B8:L1] % product_3(multiply_2(inverse_1(x0),identity_0()),x0,identity_0()) ....... U129 % ~product_3(x0, x1, multiply_2(inverse_1(x2), identity_0())) | product_3(x0, multiply_2(x1, x2), identity_0()) ....... R2 [R1:L0, U129:L0] % product_3(identity_0(),x0,multiply_2(inverse_1(inverse_1(x0)),identity_0())) ....... U48 % product_3(identity_0(), multiply_2(x0, inverse_1(x0)), identity_0()) ....... R3 [R2:L0, U48:L0] % Derivation of the empty clause: % product_3(identity_0(),multiply_2(x0,inverse_1(x0)),identity_0()) ....... U348 % ~product_3(identity_0(),multiply_2(c_0(),inverse_1(c_0())),identity_0()) ....... U199 % [] ....... R1 [U348:L0, U199:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 58137 % resolvents: 58094 factors: 43 % Number of unit clauses generated: 57025 % % unit clauses generated to total clauses generated: 98.09 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 5 [2] = 32 [3] = 312 % Total = 349 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 57025 [2] = 1079 [3] = 33 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] equalish_2 (+)15 (-)4 % [1] product_3 (+)238 (-)92 % ------------------ % Total: (+)253 (-)96 % Total number of unit clauses retained: 349 % Number of clauses skipped because of their length: 1984 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 58173 % Number of unification failures: 105351 % Number of unit to unit unification failures: 21891 % N literal unification failure due to lookup root_id table: 58 % N base clause resolution failure due to lookup table: 14 % 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: 56626 % N unit clauses dropped because too much nesting: 12589 % 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: 948 % Total number of terms of all unit clauses in table: 2480 % 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: 0.38 % Number of symbols (columns) in UCFA: 42 % Profile 2: Number of calls to: % ============================== % PTUnify() = 163524 % ConstructUnitClause() = 56970 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.08 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 0 secs % CPU time: 0.32 secs % %------------------------------------------------------------------------------