%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : NUM016-2 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art04.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 03:06:17 EST 2010 % Result : Unsatisfiable 0.14s % Output : Refutation 0.14s % 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/SystemOnTPTP16124/NUM/NUM016-2+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 = 1 secs [nr = 12] [nf = 2] [nu = 9] [ut = 5] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 46] [nf = 4] [nu = 20] [ut = 5] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 206] [nf = 8] [nu = 50] [ut = 9] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~prime_1(x0) | ~less_2(a_0(),x0) | less_2(factorial_plus_one_1(a_0()),x0) % B3: ~less_2(x1,x0) | ~less_2(x0,x1) % B5: prime_1(x0) | prime_1(prime_divisor_1(x0)) % B6: prime_1(x0) | divides_2(prime_divisor_1(x0),x0) % B7: prime_1(x0) | less_2(prime_divisor_1(x0),x0) % Unit Clauses: % -------------- % U0: < d0 v2 dv1 f0 c0 t2 td1 b > ~less_2(x0,x0) % U1: < d0 v2 dv1 f1 c0 t3 td2 b > less_2(x0,factorial_plus_one_1(x0)) % U5: < d3 v0 dv0 f2 c1 t3 td3 > prime_1(prime_divisor_1(factorial_plus_one_1(a_0()))) % U6: < d3 v0 dv0 f3 c2 t5 td3 > divides_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) % U7: < d3 v0 dv0 f3 c2 t5 td3 > less_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) % U9: < d4 v0 dv0 f3 c2 t5 td3 > ~divides_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) % --------------- Start of Proof --------------- % Derivation of unit clause U0: % ~less_2(x0,x0) ....... U0 % Derivation of unit clause U1: % less_2(x0,factorial_plus_one_1(x0)) ....... U1 % Derivation of unit clause U5: % ~prime_1(x0) | ~less_2(a_0(),x0) | less_2(factorial_plus_one_1(a_0()),x0) ....... B0 % prime_1(x0) | prime_1(prime_divisor_1(x0)) ....... B5 % ~less_2(a_0(), x0) | less_2(factorial_plus_one_1(a_0()), x0) | prime_1(prime_divisor_1(x0)) ....... R1 [B0:L0, B5:L0] % less_2(x0,factorial_plus_one_1(x0)) ....... U1 % less_2(factorial_plus_one_1(a_0()), factorial_plus_one_1(a_0())) | prime_1(prime_divisor_1(factorial_plus_one_1(a_0()))) ....... R2 [R1:L0, U1:L0] % ~less_2(x0,x0) ....... U0 % prime_1(prime_divisor_1(factorial_plus_one_1(a_0()))) ....... R3 [R2:L0, U0:L0] % Derivation of unit clause U6: % ~prime_1(x0) | ~less_2(a_0(),x0) | less_2(factorial_plus_one_1(a_0()),x0) ....... B0 % prime_1(x0) | divides_2(prime_divisor_1(x0),x0) ....... B6 % ~less_2(a_0(), x0) | less_2(factorial_plus_one_1(a_0()), x0) | divides_2(prime_divisor_1(x0), x0) ....... R1 [B0:L0, B6:L0] % less_2(x0,factorial_plus_one_1(x0)) ....... U1 % less_2(factorial_plus_one_1(a_0()), factorial_plus_one_1(a_0())) | divides_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R2 [R1:L0, U1:L0] % ~less_2(x0,x0) ....... U0 % divides_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R3 [R2:L0, U0:L0] % Derivation of unit clause U7: % ~prime_1(x0) | ~less_2(a_0(),x0) | less_2(factorial_plus_one_1(a_0()),x0) ....... B0 % prime_1(x0) | less_2(prime_divisor_1(x0),x0) ....... B7 % ~less_2(a_0(), x0) | less_2(factorial_plus_one_1(a_0()), x0) | less_2(prime_divisor_1(x0), x0) ....... R1 [B0:L0, B7:L0] % less_2(x0,factorial_plus_one_1(x0)) ....... U1 % less_2(factorial_plus_one_1(a_0()), factorial_plus_one_1(a_0())) | less_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R2 [R1:L0, U1:L0] % ~less_2(x0,x0) ....... U0 % less_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R3 [R2:L0, U0:L0] % Derivation of unit clause U9: % ~prime_1(x0) | ~less_2(a_0(),x0) | less_2(factorial_plus_one_1(a_0()),x0) ....... B0 % ~less_2(x1,x0) | ~less_2(x0,x1) ....... B3 % ~prime_1(x0) | ~less_2(a_0(), x0) | ~less_2(x0, factorial_plus_one_1(a_0())) ....... R1 [B0:L2, B3:L0] % prime_1(prime_divisor_1(factorial_plus_one_1(a_0()))) ....... U5 % ~less_2(a_0(), prime_divisor_1(factorial_plus_one_1(a_0()))) | ~less_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R2 [R1:L0, U5:L0] % ~divides_2(x0,factorial_plus_one_1(x1)) | less_2(x1,x0) ....... B4 % ~less_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) | ~divides_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R3 [R2:L0, B4:L1] % less_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) ....... U7 % ~divides_2(prime_divisor_1(factorial_plus_one_1(a_0())), factorial_plus_one_1(a_0())) ....... R4 [R3:L0, U7:L0] % Derivation of the empty clause: % ~divides_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) ....... U9 % divides_2(prime_divisor_1(factorial_plus_one_1(a_0())),factorial_plus_one_1(a_0())) ....... U6 % [] ....... R1 [U9:L0, U6:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 223 % resolvents: 215 factors: 8 % Number of unit clauses generated: 52 % % unit clauses generated to total clauses generated: 23.32 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [1] = 3 [3] = 4 % [4] = 1 % Total = 10 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 52 [2] = 112 [3] = 59 % Average size of a generated clause: 3.0 % Number of unit clauses per predicate list: % ========================================== % [0] prime_1 (+)1 (-)0 % [1] divides_2 (+)1 (-)4 % [2] less_2 (+)2 (-)2 % ------------------ % Total: (+)4 (-)6 % Total number of unit clauses retained: 10 % Number of clauses skipped because of their length: 81 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 236 % Number of unification failures: 108 % Number of unit to unit unification failures: 7 % N literal unification failure due to lookup root_id table: 468 % N base clause resolution failure due to lookup table: 274 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 6 % N unit clauses dropped because they exceeded max values: 16 % 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: 4 % Number of states in UCFA table: 34 % Total number of terms of all unit clauses in table: 38 % 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: 0.89 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 344 % ConstructUnitClause() = 24 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.00 secs % -------------------------------------------------------- % | | % Inferences per sec: inf % | | % -------------------------------------------------------- % Elapsed time: 1 secs % CPU time: 0.14 secs % %------------------------------------------------------------------------------