%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL088-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art07.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 23:55:23 EST 2010 % Result : Unsatisfiable 9.87s % Output : Refutation 9.87s % 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/SystemOnTPTP24174/LCL/LCL088-1+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 = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 136] [nf = 0] [nu = 50] [ut = 42] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 343] [nf = 6] [nu = 166] [ut = 42] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())) % B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v9 dv5 f8 c0 t17 td5 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) % U2: < d2 v9 dv5 f12 c4 t25 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))) % U3: < d2 v10 dv6 f9 c0 t19 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) % U4: < d2 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) % U5: < d2 v6 dv4 f5 c0 t11 td5 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) % U6: < d2 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) % U12: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))) % U14: < d2 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) % U791: < d4 v11 dv5 f10 c0 t21 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(x4,implies_2(implies_2(x2,x0),implies_2(x3,x0))))) % U2046: < d4 v6 dv4 f5 c0 t11 td5 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1)))) % U2081: < d4 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) % U6528: < d4 v5 dv3 f4 c0 t9 td5 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),x1))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % Derivation of unit clause U2: % ~is_a_theorem_1(implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U3: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),implies_2(x2,x4)),implies_2(x5,implies_2(x2,x4))))) ....... U3 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3)))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U5: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U4 % is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(x1, x2), implies_2(x3, x2))))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U6: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1)))) ....... R2 [R1:L0, U5:L0] % Derivation of unit clause U12: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U4 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), implies_2(implies_2(x3, x1), implies_2(x4, x1))), implies_2(x5, implies_2(implies_2(x3, x1), implies_2(x4, x1)))))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U14: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x2, x3))) | is_a_theorem_1(implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(x0,x1),implies_2(x2,x1)))) ....... U6 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x3), implies_2(implies_2(implies_2(x3, x4), x2), x3)))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U791: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), implies_2(x2, x4)), implies_2(x5, implies_2(x2, x4)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))) ....... U12 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(x4, implies_2(implies_2(x2, x0), implies_2(x3, x0))))) ....... R4 [R3:L0, U12:L0] % Derivation of unit clause U2046: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U5:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(x4,implies_2(implies_2(x2,x0),implies_2(x3,x0))))) ....... U791 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), implies_2(x3, x1)))) ....... R4 [R3:L0, U791:L0] % Derivation of unit clause U2081: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(x0, x1), implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U5:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),implies_2(x3,x1)))) ....... U2046 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0))) ....... R4 [R3:L0, U2046:L0] % Derivation of unit clause U6528: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0))))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x3, x0), implies_2(x2, x0)))), x5)) | ~is_a_theorem_1(implies_2(x5, x6)) | is_a_theorem_1(x6) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) ....... U14 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(implies_2(x2, x3), x1), x2)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U14:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) ....... U2081 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), x1))) ....... R4 [R3:L0, U2081:L0] % Derivation of the empty clause: % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x1),x1))) ....... U6528 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x3,x0),implies_2(x2,x0)))),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))) ....... U2 % [] ....... R1 [U6528:L0, U2:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 40746 % resolvents: 40736 factors: 10 % Number of unit clauses generated: 40381 % % unit clauses generated to total clauses generated: 99.10 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 40 [4] = 6487 % Total = 6529 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 40381 [2] = 354 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)637 (-)5892 % ------------------ % Total: (+)637 (-)5892 % Total number of unit clauses retained: 6529 % Number of clauses skipped because of their length: 187 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 40776 % Number of unification failures: 9631 % Number of unit to unit unification failures: 3747313 % N literal unification failure due to lookup root_id table: 26 % N base clause resolution failure due to lookup table: 0 % 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: 32917 % N unit clauses dropped because too much nesting: 4939 % 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: 63 % Max term depth in a unit clause: 11 % Number of states in UCFA table: 83508 % Total number of terms of all unit clauses in table: 337663 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.16 % Ratio n states used/total unit clauses terms: 0.25 % Number of symbols (columns) in UCFA: 38 % Profile 2: Number of calls to: % ============================== % PTUnify() = 50407 % ConstructUnitClause() = 39444 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.18 secs % -------------------------------------------------------- % | | % Inferences per sec: 4527 % | | % -------------------------------------------------------- % Elapsed time: 10 secs % CPU time: 9.86 secs % %------------------------------------------------------------------------------