%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : SYN015-2 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art01.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 08:22:52 EST 2010 % Result : Unsatisfiable 41.48s % Output : Refutation 41.48s % 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/SystemOnTPTP11391/SYN/SYN015-2+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 = 48] [nf = 0] [nu = 20] [ut = 13] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 344] [nf = 6] [nu = 146] [ut = 19] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 2288] [nf = 108] [nu = 981] [ut = 21] % Looking for a proof at depth = 4 ... % t = 0 secs [nr = 23449] [nf = 1128] [nu = 10250] [ut = 32] % Looking for a proof at depth = 5 ... % t = 1 secs [nr = 198181] [nf = 12834] [nu = 76622] [ut = 32] % Looking for a proof at depth = 6 ... % t = 4 secs [nr = 1592096] [nf = 105328] [nu = 569460] [ut = 32] % Looking for a proof at depth = 7 ... % t = 29 secs [nr = 12329458] [nf = 878745] [nu = 4111573] [ut = 32] % Looking for a proof at depth = 8 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 31 secs [nr = 13264251] [nf = 941721] [nu = 4378270] [ut = 32] % Looking for a proof at depth = 2 ... % t = 31 secs [nr = 13264658] [nf = 941727] [nu = 4378466] [ut = 32] % Looking for a proof at depth = 3 ... % t = 31 secs [nr = 13267277] [nf = 941913] [nu = 4379626] [ut = 32] % Looking for a proof at depth = 4 ... % t = 32 secs [nr = 13324106] [nf = 944062] [nu = 4402423] [ut = 36] % Looking for a proof at depth = 5 ... % t = 33 secs [nr = 14002142] [nf = 999426] [nu = 4620678] [ut = 36] % Looking for a proof at depth = 6 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~equalish_2(k_0(),a_0()) % B2: ~equalish_2(n_0(),k_0()) % B3: ~equalish_2(m_0(),n_0()) % B8: ~equalish_2(x0,n_0()) | element_2(x0,k_0()) | equalish_2(x0,k_0()) % B11: ~element_2(x0,m_0()) | ~equalish_2(f_1(x0),x0) | equalish_2(x0,m_0()) % B17: ~element_2(x0,k_0()) | equalish_2(x0,n_0()) | equalish_2(x0,m_0()) | equalish_2(x0,k_0()) % B18: ~element_2(x1,x0) | ~element_2(x0,x1) | element_2(x1,m_0()) | equalish_2(x0,x1) | equalish_2(x0,m_0()) | equalish_2(x1,m_0()) % B20: equalish_2(m_0(),k_0()) % B22: ~equalish_2(x0,x1) | equalish_2(x1,x0) % B24: ~element_2(x2,x0) | ~equalish_2(x0,x1) | element_2(x2,x1) % B25: ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) % Unit Clauses: % -------------- % U3: < d0 v0 dv0 f0 c2 t2 td1 b nc > ~equalish_2(m_0(),n_0()) % U5: < d0 v0 dv0 f0 c2 t2 td1 b nc > equalish_2(m_0(),k_0()) % U6: < d0 v2 dv1 f0 c0 t2 td1 b > equalish_2(x0,x0) % U10: < d1 v0 dv0 f0 c2 t2 td1 > ~equalish_2(n_0(),m_0()) % U16: < d2 v0 dv0 f0 c2 t2 td1 > element_2(n_0(),k_0()) % U20: < d3 v0 dv0 f0 c2 t2 td1 > element_2(n_0(),m_0()) % U21: < d4 v0 dv0 f1 c2 t3 td2 > element_2(n_0(),f_1(n_0())) % U22: < d4 v0 dv0 f1 c2 t3 td2 > element_2(f_1(n_0()),n_0()) % U23: < d4 v0 dv0 f1 c2 t3 td2 > ~equalish_2(f_1(n_0()),n_0()) % U24: < d4 v0 dv0 f1 c2 t3 td2 > ~equalish_2(f_1(n_0()),m_0()) % U26: < d4 v0 dv0 f1 c2 t3 td2 > ~equalish_2(n_0(),f_1(n_0())) % U29: < d4 v0 dv0 f1 c2 t3 td2 > ~equalish_2(f_1(n_0()),k_0()) % U33: < d4 v0 dv0 f1 c2 t3 td2 > ~element_2(f_1(n_0()),k_0()) % U35: < d4 v0 dv0 f1 c2 t3 td2 > ~element_2(f_1(n_0()),m_0()) % U36: < d6 v0 dv0 f1 c2 t3 td2 > equalish_2(f_1(n_0()),n_0()) % --------------- Start of Proof --------------- % Derivation of unit clause U3: % ~equalish_2(m_0(),n_0()) ....... U3 % Derivation of unit clause U5: % equalish_2(m_0(),k_0()) ....... U5 % Derivation of unit clause U6: % equalish_2(x0,x0) ....... U6 % Derivation of unit clause U10: % ~equalish_2(m_0(),n_0()) ....... B3 % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~equalish_2(n_0(), m_0()) ....... R1 [B3:L0, B22:L1] % Derivation of unit clause U16: % ~equalish_2(n_0(),k_0()) ....... B2 % ~equalish_2(x0,n_0()) | element_2(x0,k_0()) | equalish_2(x0,k_0()) ....... B8 % ~equalish_2(n_0(), n_0()) | element_2(n_0(), k_0()) ....... R1 [B2:L0, B8:L2] % equalish_2(x0,x0) ....... U6 % element_2(n_0(), k_0()) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U20: % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~element_2(x2,x0) | ~equalish_2(x0,x1) | element_2(x2,x1) ....... B24 % ~equalish_2(x0, x1) | ~element_2(x2, x1) | element_2(x2, x0) ....... R1 [B22:L1, B24:L1] % equalish_2(m_0(),k_0()) ....... U5 % ~element_2(x0, k_0()) | element_2(x0, m_0()) ....... R2 [R1:L0, U5:L0] % element_2(n_0(),k_0()) ....... U16 % element_2(n_0(), m_0()) ....... R3 [R2:L0, U16:L0] % Derivation of unit clause U21: % ~equalish_2(n_0(),k_0()) ....... B2 % ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) ....... B25 % ~equalish_2(x0, k_0()) | ~equalish_2(n_0(), x0) ....... R1 [B2:L0, B25:L2] % ~element_2(x0,m_0()) | element_2(x0,f_1(x0)) | equalish_2(x0,m_0()) ....... B9 % ~equalish_2(m_0(), k_0()) | ~element_2(n_0(), m_0()) | element_2(n_0(), f_1(n_0())) ....... R2 [R1:L1, B9:L2] % equalish_2(m_0(),k_0()) ....... U5 % ~element_2(n_0(), m_0()) | element_2(n_0(), f_1(n_0())) ....... R3 [R2:L0, U5:L0] % element_2(n_0(),m_0()) ....... U20 % element_2(n_0(), f_1(n_0())) ....... R4 [R3:L0, U20:L0] % Derivation of unit clause U22: % ~equalish_2(n_0(),k_0()) ....... B2 % ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) ....... B25 % ~equalish_2(x0, k_0()) | ~equalish_2(n_0(), x0) ....... R1 [B2:L0, B25:L2] % ~element_2(x0,m_0()) | element_2(f_1(x0),x0) | equalish_2(x0,m_0()) ....... B10 % ~equalish_2(m_0(), k_0()) | ~element_2(n_0(), m_0()) | element_2(f_1(n_0()), n_0()) ....... R2 [R1:L1, B10:L2] % equalish_2(m_0(),k_0()) ....... U5 % ~element_2(n_0(), m_0()) | element_2(f_1(n_0()), n_0()) ....... R3 [R2:L0, U5:L0] % element_2(n_0(),m_0()) ....... U20 % element_2(f_1(n_0()), n_0()) ....... R4 [R3:L0, U20:L0] % Derivation of unit clause U23: % ~equalish_2(n_0(),k_0()) ....... B2 % ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) ....... B25 % ~equalish_2(x0, k_0()) | ~equalish_2(n_0(), x0) ....... R1 [B2:L0, B25:L2] % ~element_2(x0,m_0()) | ~equalish_2(f_1(x0),x0) | equalish_2(x0,m_0()) ....... B11 % ~equalish_2(m_0(), k_0()) | ~element_2(n_0(), m_0()) | ~equalish_2(f_1(n_0()), n_0()) ....... R2 [R1:L1, B11:L2] % equalish_2(m_0(),k_0()) ....... U5 % ~element_2(n_0(), m_0()) | ~equalish_2(f_1(n_0()), n_0()) ....... R3 [R2:L0, U5:L0] % element_2(n_0(),m_0()) ....... U20 % ~equalish_2(f_1(n_0()), n_0()) ....... R4 [R3:L0, U20:L0] % Derivation of unit clause U24: % ~equalish_2(n_0(),k_0()) ....... B2 % ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) ....... B25 % ~equalish_2(x0, k_0()) | ~equalish_2(n_0(), x0) ....... R1 [B2:L0, B25:L2] % ~element_2(x0,m_0()) | ~equalish_2(f_1(x0),m_0()) | equalish_2(x0,m_0()) ....... B12 % ~equalish_2(m_0(), k_0()) | ~element_2(n_0(), m_0()) | ~equalish_2(f_1(n_0()), m_0()) ....... R2 [R1:L1, B12:L2] % equalish_2(m_0(),k_0()) ....... U5 % ~element_2(n_0(), m_0()) | ~equalish_2(f_1(n_0()), m_0()) ....... R3 [R2:L0, U5:L0] % element_2(n_0(),m_0()) ....... U20 % ~equalish_2(f_1(n_0()), m_0()) ....... R4 [R3:L0, U20:L0] % Derivation of unit clause U26: % ~element_2(x0,m_0()) | ~equalish_2(f_1(x0),x0) | equalish_2(x0,m_0()) ....... B11 % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~element_2(x0, m_0()) | ~equalish_2(f_1(x0), x0) | equalish_2(m_0(), x0) ....... R1 [B11:L2, B22:L0] % element_2(n_0(),m_0()) ....... U20 % ~equalish_2(f_1(n_0()), n_0()) | equalish_2(m_0(), n_0()) ....... R2 [R1:L0, U20:L0] % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % equalish_2(m_0(), n_0()) | ~equalish_2(n_0(), f_1(n_0())) ....... R3 [R2:L0, B22:L1] % ~equalish_2(m_0(),n_0()) ....... U3 % ~equalish_2(n_0(), f_1(n_0())) ....... R4 [R3:L0, U3:L0] % Derivation of unit clause U29: % equalish_2(m_0(),k_0()) ....... B20 % ~equalish_2(x1,x2) | ~equalish_2(x0,x1) | equalish_2(x0,x2) ....... B25 % ~equalish_2(k_0(), x0) | equalish_2(m_0(), x0) ....... R1 [B20:L0, B25:L1] % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~equalish_2(k_0(), x0) | equalish_2(x0, m_0()) ....... R2 [R1:L1, B22:L0] % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % equalish_2(x0, m_0()) | ~equalish_2(x0, k_0()) ....... R3 [R2:L0, B22:L1] % ~equalish_2(f_1(n_0()),m_0()) ....... U24 % ~equalish_2(f_1(n_0()), k_0()) ....... R4 [R3:L0, U24:L0] % Derivation of unit clause U33: % ~element_2(x0,k_0()) | equalish_2(x0,n_0()) | equalish_2(x0,m_0()) | equalish_2(x0,k_0()) ....... B17 % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~element_2(x0, k_0()) | equalish_2(x0, m_0()) | equalish_2(x0, k_0()) | equalish_2(n_0(), x0) ....... R1 [B17:L1, B22:L0] % ~equalish_2(f_1(n_0()),m_0()) ....... U24 % ~element_2(f_1(n_0()), k_0()) | equalish_2(f_1(n_0()), k_0()) | equalish_2(n_0(), f_1(n_0())) ....... R2 [R1:L1, U24:L0] % ~equalish_2(f_1(n_0()),k_0()) ....... U29 % ~element_2(f_1(n_0()), k_0()) | equalish_2(n_0(), f_1(n_0())) ....... R3 [R2:L1, U29:L0] % ~equalish_2(n_0(),f_1(n_0())) ....... U26 % ~element_2(f_1(n_0()), k_0()) ....... R4 [R3:L1, U26:L0] % Derivation of unit clause U35: % equalish_2(m_0(),k_0()) ....... B20 % ~element_2(x2,x0) | ~equalish_2(x0,x1) | element_2(x2,x1) ....... B24 % ~element_2(x0, m_0()) | element_2(x0, k_0()) ....... R1 [B20:L0, B24:L1] % ~element_2(x0,x1) | ~equalish_2(x0,x2) | element_2(x2,x1) ....... B23 % ~element_2(x0, m_0()) | ~equalish_2(x0, x1) | element_2(x1, k_0()) ....... R2 [R1:L1, B23:L0] % equalish_2(x0,x0) ....... U6 % ~element_2(x0, m_0()) | element_2(x0, k_0()) ....... R3 [R2:L1, U6:L0] % ~element_2(f_1(n_0()),k_0()) ....... U33 % ~element_2(f_1(n_0()), m_0()) ....... R4 [R3:L1, U33:L0] % Derivation of unit clause U36: % ~element_2(x1,x0) | ~element_2(x0,x1) | element_2(x1,m_0()) | equalish_2(x0,x1) | equalish_2(x0,m_0()) | equalish_2(x1,m_0()) ....... B18 % ~equalish_2(x0,x1) | equalish_2(x1,x0) ....... B22 % ~element_2(x0, x1) | ~element_2(x1, x0) | element_2(x0, m_0()) | equalish_2(x1, m_0()) | equalish_2(x0, m_0()) | equalish_2(x0, x1) ....... R1 [B18:L3, B22:L0] % element_2(f_1(n_0()),n_0()) ....... U22 % ~element_2(n_0(), f_1(n_0())) | element_2(f_1(n_0()), m_0()) | equalish_2(n_0(), m_0()) | equalish_2(f_1(n_0()), m_0()) | equalish_2(f_1(n_0()), n_0()) ....... R2 [R1:L0, U22:L0] % element_2(n_0(),f_1(n_0())) ....... U21 % element_2(f_1(n_0()), m_0()) | equalish_2(n_0(), m_0()) | equalish_2(f_1(n_0()), m_0()) | equalish_2(f_1(n_0()), n_0()) ....... R3 [R2:L0, U21:L0] % ~element_2(f_1(n_0()),m_0()) ....... U35 % equalish_2(n_0(), m_0()) | equalish_2(f_1(n_0()), m_0()) | equalish_2(f_1(n_0()), n_0()) ....... R4 [R3:L0, U35:L0] % ~equalish_2(n_0(),m_0()) ....... U10 % equalish_2(f_1(n_0()), m_0()) | equalish_2(f_1(n_0()), n_0()) ....... R5 [R4:L0, U10:L0] % ~equalish_2(f_1(n_0()),m_0()) ....... U24 % equalish_2(f_1(n_0()), n_0()) ....... R6 [R5:L0, U24:L0] % Derivation of the empty clause: % equalish_2(f_1(n_0()),n_0()) ....... U36 % ~equalish_2(f_1(n_0()),n_0()) ....... U23 % [] ....... R1 [U36:L0, U23:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 18488533 % resolvents: 17332788 factors: 1155745 % Number of unit clauses generated: 5130730 % % unit clauses generated to total clauses generated: 27.75 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 7 [1] = 6 [2] = 6 [3] = 2 % [4] = 15 [6] = 1 % Total = 37 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 5130730 [2] = 7762891 [3] = 5146510 [4] = 398617 [5] = 47388 [6] = 2313 % [7] = 84 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] element_2 (+)6 (-)6 % [1] equalish_2 (+)7 (-)18 % ------------------ % Total: (+)13 (-)24 % Total number of unit clauses retained: 37 % Number of clauses skipped because of their length: 51370506 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 18488577 % Number of unification failures: 59061287 % Number of unit to unit unification failures: 154 % N literal unification failure due to lookup root_id table: 39791188 % N base clause resolution failure due to lookup table: 866975 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 16 % N unit clauses dropped because they exceeded max values: 4473546 % 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: 3 % Max term depth in a unit clause: 2 % Number of states in UCFA table: 33 % Total number of terms of all unit clauses in table: 88 % 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: 0.38 % Number of symbols (columns) in UCFA: 42 % Profile 2: Number of calls to: % ============================== % PTUnify() = 77549864 % ConstructUnitClause() = 4473576 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 4.47 secs % -------------------------------------------------------- % | | % Inferences per sec: 450940 % | | % -------------------------------------------------------- % Elapsed time: 42 secs % CPU time: 41.49 secs % %------------------------------------------------------------------------------