%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL091-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art03.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 23:55:49 EST 2010 % Result : Unsatisfiable 173.71s % Output : Refutation 173.71s % 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/SystemOnTPTP23983/LCL/LCL091-1+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 = 58] [nf = 0] [nu = 20] [ut = 18] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 139] [nf = 4] [nu = 58] [ut = 18] % Looking for a proof at depth = 4 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 123 secs [nr = 465868] [nf = 8] [nu = 444398] [ut = 18094] % Looking for a proof at depth = 2 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(implies_2(a_0(),implies_2(b_0(),a_0()))) % B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) % U3: < d2 v10 dv6 f9 c0 t19 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3))))) % U6: < d2 v12 dv7 f11 c0 t23 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1)))))) % U7: < d2 v14 dv8 f13 c0 t27 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) % U8: < d2 v15 dv9 f14 c0 t29 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,x3))),implies_2(x4,implies_2(x5,implies_2(x6,x2)))),implies_2(x7,implies_2(x8,implies_2(x4,implies_2(x5,implies_2(x6,x2))))))) % U18: < d4 v1 dv1 f8 c8 t17 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(x0,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))) % U145: < d4 v11 dv7 f18 c8 t37 td7 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3)))),implies_2(implies_2(implies_2(x6,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))) % U187: < d4 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))))))) % U205: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x1,implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,implies_2(x4,x3)))))) % U217: < d4 v13 dv7 f12 c0 t25 td6 > is_a_theorem_1(implies_2(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5))))) % U319: < d4 v11 dv7 f10 c0 t21 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,implies_2(implies_2(x3,x0),x0))),x4),implies_2(x5,implies_2(x6,x4)))) % U15258: < d4 v17 dv10 f24 c8 t49 td8 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,implies_2(x4,x5)),implies_2(x5,x6)),implies_2(x7,implies_2(implies_2(x8,x5),implies_2(x5,x6)))),implies_2(implies_2(implies_2(x9,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))))) % U16958: < d4 v23 dv13 f30 c8 t61 td9 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))),implies_2(implies_2(implies_2(implies_2(x6,implies_2(x7,x8)),implies_2(x8,x9)),implies_2(x10,implies_2(implies_2(x11,x8),implies_2(x8,x9)))),implies_2(implies_2(implies_2(x12,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))))) % U22753: < d2 v11 dv7 f10 c0 t21 td7 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,x4)),implies_2(x5,implies_2(x6,implies_2(x3,x4))))))) % U23556: < d2 v10 dv6 f9 c0 t19 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,x3)),implies_2(x4,implies_2(x5,implies_2(x2,x3)))))) % --------------- 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(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1 % Derivation of unit clause U3: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U6: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3))))) ....... U3 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(x4, x1))), implies_2(x5, implies_2(x6, implies_2(x3, implies_2(x4, x1)))))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U7: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1)))))) ....... U6 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, implies_2(x2, x3))), implies_2(implies_2(x4, x3), implies_2(x3, x5))), implies_2(x6, implies_2(x7, implies_2(implies_2(x4, x3), implies_2(x3, x5)))))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U8: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, implies_2(x2, x0)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(implies_2(x1, x2), implies_2(x2, x3))), implies_2(x4, implies_2(x5, implies_2(x6, x2)))), implies_2(x7, implies_2(x8, implies_2(x4, implies_2(x5, implies_2(x6, x2))))))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U18: % ~is_a_theorem_1(implies_2(a_0(),implies_2(b_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(a_0(), implies_2(b_0(), a_0())))) ....... R1 [B0:L0, B2:L2] % ~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(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, x0)) ....... R2 [R1:L0, B2:L2] % ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) | ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0()))), x0)) ....... R3 [R2:L0, R2:L1] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x4,x1))),implies_2(x5,implies_2(x6,implies_2(x3,implies_2(x4,x1)))))) ....... U6 % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R4 [R3:L1, U6:L0] % Derivation of unit clause U145: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0] % ~is_a_theorem_1(implies_2(implies_2(implies_2(x0,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))) ....... U18 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x2, x3)), implies_2(x4, implies_2(implies_2(x5, x2), implies_2(x2, x3)))), implies_2(implies_2(implies_2(x6, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0()))))) ....... R4 [R3:L1, U18:L0] % Derivation of unit clause U187: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3))))) ....... U3 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(x1, x2), implies_2(x2, implies_2(implies_2(implies_2(x3, x4), x4), implies_2(x4, implies_2(x5, x4))))))) ....... R4 [R3:L0, U3:L0] % Derivation of unit clause U205: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(x1,x2),implies_2(x2,implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))))))) ....... U187 % is_a_theorem_1(implies_2(implies_2(x0, x1), implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3)))))) ....... R4 [R3:L0, U187:L0] % Derivation of unit clause U217: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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,implies_2(x1,implies_2(x2,x3))),implies_2(implies_2(x4,x3),implies_2(x3,x5))),implies_2(x6,implies_2(x7,implies_2(implies_2(x4,x3),implies_2(x3,x5)))))) ....... U7 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, implies_2(x4, x3))))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(implies_2(implies_2(x0,x1),implies_2(x1,implies_2(implies_2(implies_2(x2,x3),x3),implies_2(x3,implies_2(x4,x3)))))) ....... U205 % is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x2), implies_2(x2, implies_2(x3, x2)))), implies_2(implies_2(implies_2(x4, x5), x5), implies_2(x5, implies_2(x6, x5))))) ....... R4 [R3:L0, U205:L0] % Derivation of unit clause U319: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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,implies_2(implies_2(x1,x2),implies_2(x2,x3))),implies_2(x4,implies_2(x5,implies_2(x6,x2)))),implies_2(x7,implies_2(x8,implies_2(x4,implies_2(x5,implies_2(x6,x2))))))) ....... U8 % ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(x2, x3), x2), implies_2(x4, implies_2(implies_2(x5, x2), x2))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U8:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,implies_2(x2,x0))))) ....... U1 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, implies_2(implies_2(x3, x0), x0))), x4), implies_2(x5, implies_2(x6, x4)))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U15258: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5))))) ....... U217 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U217:L0] % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x2,x3)),implies_2(x4,implies_2(implies_2(x5,x2),implies_2(x2,x3)))),implies_2(implies_2(implies_2(x6,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))) ....... U145 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), implies_2(implies_2(implies_2(implies_2(x3, implies_2(x4, x5)), implies_2(x5, x6)), implies_2(x7, implies_2(implies_2(x8, x5), implies_2(x5, x6)))), implies_2(implies_2(implies_2(x9, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0())))))) ....... R4 [R3:L1, U145:L0] % Derivation of unit clause U16958: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x3, x0), implies_2(x4, 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(x0,implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,implies_2(x3,x2)))),implies_2(implies_2(implies_2(x4,x5),x5),implies_2(x5,implies_2(x6,x5))))) ....... U217 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U217:L0] % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,implies_2(x4,x5)),implies_2(x5,x6)),implies_2(x7,implies_2(implies_2(x8,x5),implies_2(x5,x6)))),implies_2(implies_2(implies_2(x9,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0())))))) ....... U15258 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x1), implies_2(x1, implies_2(x2, x1))), implies_2(implies_2(implies_2(implies_2(x3, x4), x4), implies_2(x4, implies_2(x5, x4))), implies_2(implies_2(implies_2(implies_2(x6, implies_2(x7, x8)), implies_2(x8, x9)), implies_2(x10, implies_2(implies_2(x11, x8), implies_2(x8, x9)))), implies_2(implies_2(implies_2(x12, a_0()), implies_2(a_0(), implies_2(a_0(), implies_2(b_0(), a_0())))), implies_2(a_0(), implies_2(b_0(), a_0()))))))) ....... R4 [R3:L1, U15258:L0] % Derivation of unit clause U22753: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(x0,x1),x0),implies_2(x2,implies_2(implies_2(x3,x0),x0))),x4),implies_2(x5,implies_2(x6,x4)))) ....... U319 % is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(implies_2(x2, x3), x3), implies_2(x3, x4)), implies_2(x5, implies_2(x6, implies_2(x3, x4))))))) ....... R2 [R1:L0, U319:L0] % Derivation of unit clause U23556: % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),implies_2(implies_2(x3,x0),implies_2(x4,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(implies_2(x3, x0), implies_2(x4, 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(implies_2(implies_2(x2,x3),x3),implies_2(x3,x4)),implies_2(x5,implies_2(x6,implies_2(x3,x4))))))) ....... U22753 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), x2), implies_2(x2, x3)), implies_2(x4, implies_2(x5, implies_2(x2, x3)))))) ....... R2 [R1:L0, U22753:L0] % Derivation of the empty clause: % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),x2),implies_2(x2,x3)),implies_2(x4,implies_2(x5,implies_2(x2,x3)))))) ....... U23556 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x1),implies_2(x1,implies_2(x2,x1))),implies_2(implies_2(implies_2(implies_2(x3,x4),x4),implies_2(x4,implies_2(x5,x4))),implies_2(implies_2(implies_2(implies_2(x6,implies_2(x7,x8)),implies_2(x8,x9)),implies_2(x10,implies_2(implies_2(x11,x8),implies_2(x8,x9)))),implies_2(implies_2(implies_2(x12,a_0()),implies_2(a_0(),implies_2(a_0(),implies_2(b_0(),a_0())))),implies_2(a_0(),implies_2(b_0(),a_0()))))))) ....... U16958 % [] ....... R1 [U23556:L0, U16958:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 473860 % resolvents: 473852 factors: 8 % Number of unit clauses generated: 452380 % % unit clauses generated to total clauses generated: 95.47 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 5479 [4] = 18076 % Total = 23557 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 452380 [2] = 21467 [3] = 13 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)5525 (-)18032 % ------------------ % Total: (+)5525 (-)18032 % Total number of unit clauses retained: 23557 % Number of clauses skipped because of their length: 143 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 473904 % Number of unification failures: 82713 % Number of unit to unit unification failures: 99621357 % N literal unification failure due to lookup root_id table: 34 % 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: 23 % N unit clauses dropped because they exceeded max values: 428668 % N unit clauses dropped because too much nesting: 11342 % 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: 347657 % Total number of terms of all unit clauses in table: 1115985 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.66 % Ratio n states used/total unit clauses terms: 0.31 % Number of symbols (columns) in UCFA: 38 % Profile 2: Number of calls to: % ============================== % PTUnify() = 556617 % ConstructUnitClause() = 452223 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 2.42 secs % -------------------------------------------------------- % | | % Inferences per sec: 2739 % | | % -------------------------------------------------------- % Elapsed time: 176 secs % CPU time: 173.67 secs % %------------------------------------------------------------------------------