%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL094-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art06.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 23:56:24 EST 2010 % Result : Unsatisfiable 173.16s % Output : Refutation 173.16s % 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/SystemOnTPTP22558/LCL/LCL094-1+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 = 344] [nf = 6] [nu = 167] [ut = 42] % Looking for a proof at depth = 4 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 153 secs [nr = 388709] [nf = 10] [nu = 367536] [ut = 18263] % 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(implies_2(a_0(),b_0()),b_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))))) % 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)))) % U11: < d2 v12 dv7 f11 c0 t23 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,implies_2(x2,x3)),x4),implies_2(implies_2(implies_2(implies_2(x5,x2),implies_2(x6,x2)),implies_2(x2,x3)),x4)))) % 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)))))) % U13: < d2 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(x1,x4)))) % 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)))) % U19: < d2 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x5,x4)),x2),x3)))) % U20: < d2 v10 dv6 f9 c0 t19 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) % U26: < d2 v12 dv7 f11 c0 t23 td8 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) % U32: < d2 v14 dv8 f13 c0 t27 td9 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(x7,x3),x1),x4),x5),x6)))) % U38: < d2 v16 dv9 f15 c0 t31 td10 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),x6),x7),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3,x8),x2),x3),x4),x5),x6),x7)))) % U819: < d4 v11 dv6 f10 c0 t21 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) % U827: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(implies_2(implies_2(x0,x3),implies_2(x4,x3)),x1),x2))) % U843: < d4 v15 dv8 f14 c0 t29 td9 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2,x7),x1),x2),x3),x4),x5),x6))) % U2051: < d4 v10 dv6 f9 c0 t19 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(implies_2(x0,x3),x4),implies_2(x5,x4)))) % U2085: < d4 v11 dv7 f10 c0 t21 td8 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(x4,x3))),x5),implies_2(x6,x5))) % U4293: < d4 v10 dv7 f9 c0 t19 td8 > is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(implies_2(x2,x3),x4),implies_2(x5,x4)),x2),implies_2(x6,x2))))) % U4315: < d4 v9 dv6 f8 c0 t17 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),implies_2(x4,x3)),x1),implies_2(x5,x1)))) % U4322: < d4 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(x3,x2)),x0),implies_2(x4,x0))) % U9315: < d4 v13 dv7 f12 c0 t25 td8 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(x4,x2)),x5),implies_2(implies_2(implies_2(x6,x3),implies_2(x4,x2)),x5))) % U9574: < d4 v11 dv6 f10 c0 t21 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x4)),implies_2(implies_2(implies_2(x5,x1),implies_2(x1,x2)),implies_2(x3,x4)))) % U11829: < d4 v9 dv5 f8 c0 t17 td7 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x4)),x1),x4),implies_2(x3,x4)))) % U12075: < d4 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),x0),x3),implies_2(x2,x3))) % U15291: < d4 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(implies_2(x2,x4),implies_2(x1,x4))))) % U15599: < d4 v9 dv5 f8 c0 t17 td6 > is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(implies_2(x3,x1),x4)))) % U15675: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3))) % U21769: < d2 v8 dv4 f11 c4 t23 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3)),implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_0())))) % --------------- 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 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 U11: % 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(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(x0, implies_2(implies_2(implies_2(x1, implies_2(x2, x3)), x4), implies_2(implies_2(implies_2(implies_2(x5, x2), implies_2(x6, x2)), implies_2(x2, x3)), x4)))) ....... R2 [R1:L0, U3: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 U13: % 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(x1,implies_2(implies_2(x1,x2),implies_2(x3,x2))))) ....... U5 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), x4), implies_2(x1, x4)))) ....... R2 [R1:L0, U5: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 U19: % 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(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(x1,x4)))) ....... U13 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x3), implies_2(implies_2(implies_2(implies_2(x1, x4), implies_2(x5, x4)), x2), x3)))) ....... R2 [R1:L0, U13:L0] % Derivation of unit clause U20: % 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(implies_2(x1,x2),x3),implies_2(implies_2(implies_2(x3,x4),x2),x3)))) ....... U14 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x1), x4), implies_2(implies_2(implies_2(x5, x3), x1), x4)))) ....... R2 [R1:L0, U14:L0] % Derivation of unit clause U26: % 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(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x4), x5), implies_2(implies_2(implies_2(implies_2(implies_2(x3, x6), x2), x3), x4), x5)))) ....... R2 [R1:L0, U20:L0] % Derivation of unit clause U32: % 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(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x1), x4), x5), x6), implies_2(implies_2(implies_2(implies_2(implies_2(x7, x3), x1), x4), x5), x6)))) ....... R2 [R1:L0, U26:L0] % Derivation of unit clause U38: % 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(implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x1),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(x7,x3),x1),x4),x5),x6)))) ....... U32 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x4), x5), x6), x7), implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3, x8), x2), x3), x4), x5), x6), x7)))) ....... R2 [R1:L0, U32:L0] % Derivation of unit clause U819: % 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,implies_2(x2,x3)),x4),implies_2(implies_2(implies_2(implies_2(x5,x2),implies_2(x6,x2)),implies_2(x2,x3)),x4)))) ....... U11 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), x3), implies_2(implies_2(implies_2(implies_2(x4, x1), implies_2(x5, x1)), implies_2(x1, x2)), x3))) ....... R4 [R3:L0, U11:L0] % Derivation of unit clause U827: % 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),x3),implies_2(implies_2(implies_2(implies_2(x1,x4),implies_2(x5,x4)),x2),x3)))) ....... U19 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(implies_2(implies_2(x0, x3), implies_2(x4, x3)), x1), x2))) ....... R4 [R3:L0, U19:L0] % Derivation of unit clause U843: % 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(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),x4),x5),x6),x7),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x3,x8),x2),x3),x4),x5),x6),x7)))) ....... U38 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), x5), x6), implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2, x7), x1), x2), x3), x4), x5), x6))) ....... R4 [R3:L0, U38:L0] % Derivation of unit clause U2051: % 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),x2),implies_2(implies_2(implies_2(implies_2(x0,x3),implies_2(x4,x3)),x1),x2))) ....... U827 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(implies_2(x0, x3), x4), implies_2(x5, x4)))) ....... R4 [R3:L0, U827:L0] % Derivation of unit clause U2085: % 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(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(implies_2(x0,x3),x4),implies_2(x5,x4)))) ....... U2051 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(x4, x3))), x5), implies_2(x6, x5))) ....... R4 [R3:L0, U2051:L0] % Derivation of unit clause U4293: % 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),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(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)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(x4,x3))),x5),implies_2(x6,x5))) ....... U2085 % is_a_theorem_1(implies_2(x0, implies_2(x1, implies_2(implies_2(implies_2(implies_2(implies_2(x2, x3), x4), implies_2(x5, x4)), x2), implies_2(x6, x2))))) ....... R4 [R3:L0, U2085:L0] % Derivation of unit clause U4315: % 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),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(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)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0] % is_a_theorem_1(implies_2(x0,implies_2(x1,implies_2(implies_2(implies_2(implies_2(implies_2(x2,x3),x4),implies_2(x5,x4)),x2),implies_2(x6,x2))))) ....... U4293 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), x3), implies_2(x4, x3)), x1), implies_2(x5, x1)))) ....... R4 [R3:L0, U4293:L0] % Derivation of unit clause U4322: % 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),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(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)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U12:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),x3),implies_2(x4,x3)),x1),implies_2(x5,x1)))) ....... U4315 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(x3, x2)), x0), implies_2(x4, x0))) ....... R4 [R3:L0, U4315:L0] % Derivation of unit clause U9315: % 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(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U20:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x3),x4),x5),x6),implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x2,x7),x1),x2),x3),x4),x5),x6))) ....... U843 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(x4, x2)), x5), implies_2(implies_2(implies_2(x6, x3), implies_2(x4, x2)), x5))) ....... R4 [R3:L0, U843:L0] % Derivation of unit clause U9574: % 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(implies_2(implies_2(x1,x2),x3),x1),x4),implies_2(implies_2(implies_2(x5,x3),x1),x4)))) ....... U20 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x0), x3), implies_2(implies_2(implies_2(x4, x2), x0), x3)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U20:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x0),x3),implies_2(x4,x2)),x5),implies_2(implies_2(implies_2(x6,x3),implies_2(x4,x2)),x5))) ....... U9315 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x3, x4)), implies_2(implies_2(implies_2(x5, x1), implies_2(x1, x2)), implies_2(x3, x4)))) ....... R4 [R3:L0, U9315:L0] % Derivation of unit clause U11829: % 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(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), implies_2(implies_2(implies_2(implies_2(implies_2(x2, x5), x1), x2), x3), x4)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U26:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(x3,x2)),x0),implies_2(x4,x0))) ....... U4322 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x4)), x1), x4), implies_2(x3, x4)))) ....... R4 [R3:L0, U4322:L0] % Derivation of unit clause U12075: % 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(implies_2(implies_2(x1,x2),x3),x4),x5),implies_2(implies_2(implies_2(implies_2(implies_2(x3,x6),x2),x3),x4),x5)))) ....... U26 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), x3), x4), implies_2(implies_2(implies_2(implies_2(implies_2(x2, x5), x1), x2), x3), x4)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U26:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x4)),x1),x4),implies_2(x3,x4)))) ....... U11829 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x3)), x0), x3), implies_2(x2, x3))) ....... R4 [R3:L0, U11829:L0] % Derivation of unit clause U15291: % 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,implies_2(x1,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x4)),implies_2(implies_2(implies_2(x5,x1),implies_2(x1,x2)),implies_2(x3,x4)))) ....... U9574 % is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(implies_2(x2, x4), implies_2(x1, x4))))) ....... R4 [R3:L0, U9574:L0] % Derivation of unit clause U15599: % 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,implies_2(x1,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0] % is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(implies_2(x2,x4),implies_2(x1,x4))))) ....... U15291 % is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), implies_2(x3, x2)), x4), implies_2(implies_2(x3, x1), x4)))) ....... R4 [R3:L0, U15291:L0] % Derivation of unit clause U15675: % 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,implies_2(x1,x2)),x3),implies_2(implies_2(implies_2(implies_2(x4,x1),implies_2(x5,x1)),implies_2(x1,x2)),x3))) ....... U819 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(implies_2(x3, x5), implies_2(x1, x5)))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U819:L0] % is_a_theorem_1(implies_2(x0,implies_2(implies_2(implies_2(implies_2(x1,x2),implies_2(x3,x2)),x4),implies_2(implies_2(x3,x1),x4)))) ....... U15599 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x2, x0), x3))) ....... R4 [R3:L0, U15599:L0] % Derivation of unit clause U21769: % ~is_a_theorem_1(implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_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(implies_2(a_0(), b_0()), b_0())))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3))) ....... U15675 % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), x3), implies_2(implies_2(x2, x0), x3)), implies_2(a_0(), implies_2(implies_2(a_0(), b_0()), b_0())))) ....... R2 [R1:L0, U15675:L0] % Derivation of the empty clause: % ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),x3),implies_2(implies_2(x2,x0),x3)),implies_2(a_0(),implies_2(implies_2(a_0(),b_0()),b_0())))) ....... U21769 % is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x3)),x0),x3),implies_2(x2,x3))) ....... U12075 % [] ....... R1 [U21769:L0, U12075:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 392367 % resolvents: 392357 factors: 10 % Number of unit clauses generated: 371183 % % unit clauses generated to total clauses generated: 94.60 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 3547 [4] = 18221 % Total = 21770 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 371183 [2] = 21171 [3] = 13 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)4322 (-)17448 % ------------------ % Total: (+)4322 (-)17448 % Total number of unit clauses retained: 21770 % Number of clauses skipped because of their length: 216 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 392455 % Number of unification failures: 55362 % Number of unit to unit unification failures: 75408151 % 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: 18 % N unit clauses dropped because they exceeded max values: 348447 % N unit clauses dropped because too much nesting: 17843 % 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: 293438 % Total number of terms of all unit clauses in table: 1024854 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.56 % Ratio n states used/total unit clauses terms: 0.29 % Number of symbols (columns) in UCFA: 38 % Profile 2: Number of calls to: % ============================== % PTUnify() = 447817 % ConstructUnitClause() = 370215 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 1.94 secs % -------------------------------------------------------- % | | % Inferences per sec: 2268 % | | % -------------------------------------------------------- % Elapsed time: 175 secs % CPU time: 173.13 secs % %------------------------------------------------------------------------------