%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL131-1 : 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 : Sun Nov 28 00:09:19 EST 2010 % Result : Unsatisfiable 139.64s % Output : Refutation 139.64s % 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/SystemOnTPTP25886/LCL/LCL131-1+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 = 0 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 77] [nf = 0] [nu = 35] [ut = 25] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 188] [nf = 5] [nu = 99] [ut = 25] % Looking for a proof at depth = 4 ... % Entering time slice 2 % Updating parameters ... done. % Looking for a proof at depth = 1 ... % t = 141 secs [nr = 185194] [nf = 9] [nu = 165220] [ut = 17355] % 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(equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v8 dv4 f7 c0 t15 td6 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) % U4: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)))) % U9: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) % U10: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(x0,x2),x3))) % U11: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),equivalent_2(x0,x3))) % U12: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),x4),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),x4))) % U13: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x3,x2)),equivalent_2(x0,x3))) % U14: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x0,x2),x4))) % U15: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) % U16: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x4,x1),x2),x3)),equivalent_2(x0,x4))) % U17: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),x4),x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),x4),x5))) % U382: < d4 v8 dv4 f7 c0 t15 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) % U388: < d4 v10 dv5 f9 c0 t19 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),equivalent_2(x2,x4)),x3))) % U519: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x1,x3)))) % U521: < d4 v10 dv5 f9 c0 t19 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x4),equivalent_2(x0,x4))) % U804: < d4 v4 dv2 f3 c0 t7 td4 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(x1,x1)))) % U806: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x6),equivalent_2(x1,x6)),x2),equivalent_2(x3,x5)))) % U1206: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),x4),equivalent_2(equivalent_2(x1,x3),x4)))) % U1399: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)),x1)))) % U1408: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x3,equivalent_2(x1,x4))),x5),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x4,x2)),x3),x5))) % U1428: < d4 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x1,x3))),equivalent_2(x4,equivalent_2(x5,x6))),equivalent_2(equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)),x4))) % U1448: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x0,equivalent_2(x5,x2)),equivalent_2(x4,equivalent_2(x5,x1))))) % U1455: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x4,x4)),equivalent_2(x1,x3)))) % U2210: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),x4),equivalent_2(x0,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x2,x5),equivalent_2(x3,x5)),x1))))) % U2681: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x4)),equivalent_2(equivalent_2(equivalent_2(x1,x5),equivalent_2(x2,x5)),equivalent_2(equivalent_2(x3,x6),equivalent_2(x4,x6)))))) % U3965: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)),equivalent_2(x2,x4))),equivalent_2(x5,x1)),equivalent_2(x6,x7)),equivalent_2(equivalent_2(equivalent_2(x0,x8),equivalent_2(x5,x8)),equivalent_2(equivalent_2(x6,x9),equivalent_2(x7,x9))))) % U4698: < d4 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),x7),equivalent_2(equivalent_2(x2,x3),x7)))) % U12468: < d4 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x4),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7))),x8),equivalent_2(equivalent_2(x0,x4),x8))) % U14456: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)))),equivalent_2(x0,x2))) % U17457: < d2 v10 dv5 f17 c8 t35 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x4,x4)),equivalent_2(x1,x3))),equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0()))))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... U1 % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)))) ....... U4 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U10: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), equivalent_2(equivalent_2(x0, x2), x3))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U11: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(x0,x2),x3))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), x2)), equivalent_2(x0, x3))) ....... R2 [R1:L0, U10:L0] % Derivation of unit clause U12: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),equivalent_2(x0,x3))) ....... U11 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), x4), equivalent_2(equivalent_2(equivalent_2(x0, x2), x3), x4))) ....... R2 [R1:L0, U11:L0] % Derivation of unit clause U13: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),x4),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),x4))) ....... U12 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x3, x2)), equivalent_2(x0, x3))) ....... R2 [R1:L0, U12:L0] % Derivation of unit clause U14: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x3,x2)),equivalent_2(x0,x3))) ....... U13 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x0, x2), x4))) ....... R2 [R1:L0, U13:L0] % Derivation of unit clause U15: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x0,x2),x4))) ....... U14 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), x2)), x4), equivalent_2(equivalent_2(x0, x3), x4))) ....... R2 [R1:L0, U14:L0] % Derivation of unit clause U16: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(x4, x1), x2), x3)), equivalent_2(x0, x4))) ....... R2 [R1:L0, U15:L0] % Derivation of unit clause U17: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x4,x1),x2),x3)),equivalent_2(x0,x4))) ....... U16 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), x4), x5), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x2), x3), x4), x5))) ....... R2 [R1:L0, U16:L0] % Derivation of unit clause U382: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(x0, x3), equivalent_2(x2, x3)))) ....... R4 [R3:L0, U9:L0] % Derivation of unit clause U388: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U382 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3), equivalent_2(equivalent_2(equivalent_2(x0, x4), equivalent_2(x2, x4)), x3))) ....... R4 [R3:L0, U382:L0] % Derivation of unit clause U519: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U9:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R4 [R3:L0, U15:L0] % Derivation of unit clause U521: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U9 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U9:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U382 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4), equivalent_2(x0, x4))) ....... R4 [R3:L0, U382:L0] % Derivation of unit clause U804: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(x0,x2),x3))) ....... U10 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U10:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x3,x2)),equivalent_2(x0,x3))) ....... U13 % is_a_theorem_1(equivalent_2(x0, equivalent_2(x0, equivalent_2(x1, x1)))) ....... R4 [R3:L0, U13:L0] % Derivation of unit clause U806: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(x0,x2),x3))) ....... U10 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2))), equivalent_2(x0, equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U10:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),x4),x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),x4),x5))) ....... U17 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x6), equivalent_2(x1, x6)), x2), equivalent_2(x3, x5)))) ....... R4 [R3:L0, U17:L0] % Derivation of unit clause U1206: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),x4),equivalent_2(equivalent_2(equivalent_2(x0,x2),x3),x4))) ....... U12 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4))), equivalent_2(equivalent_2(x0, x5), equivalent_2(x1, x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U12:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), x4), equivalent_2(equivalent_2(x1, x3), x4)))) ....... R4 [R3:L0, U15:L0] % Derivation of unit clause U1399: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x4),equivalent_2(x0,x4))) ....... U521 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)), x1)))) ....... R4 [R3:L0, U521:L0] % Derivation of unit clause U1408: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),x4),equivalent_2(equivalent_2(x1,x3),x4)))) ....... U1206 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x3, equivalent_2(x1, x4))), x5), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x4, x2)), x3), x5))) ....... R4 [R3:L0, U1206:L0] % Derivation of unit clause U1428: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x2,x4),equivalent_2(x3,x4)),x1)))) ....... U1399 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), equivalent_2(x4, equivalent_2(x5, x6))), equivalent_2(equivalent_2(equivalent_2(x5, x7), equivalent_2(x6, x7)), x4))) ....... R4 [R3:L0, U1399:L0] % Derivation of unit clause U1448: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x1,x3))),equivalent_2(x4,equivalent_2(x5,x6))),equivalent_2(equivalent_2(equivalent_2(x5,x7),equivalent_2(x6,x7)),x4))) ....... U1428 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x3), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x0, equivalent_2(x5, x2)), equivalent_2(x4, equivalent_2(x5, x1))))) ....... R4 [R3:L0, U1428:L0] % Derivation of unit clause U1455: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),x2)),x4),equivalent_2(equivalent_2(x0,x3),x4))) ....... U15 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x0,equivalent_2(x5,x2)),equivalent_2(x4,equivalent_2(x5,x1))))) ....... U1448 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x4, x4)), equivalent_2(x1, x3)))) ....... R4 [R3:L0, U1448:L0] % Derivation of unit clause U2210: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(x0,x3),equivalent_2(x2,x3)))) ....... U382 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4), equivalent_2(x0, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U382:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x3,equivalent_2(x1,x4))),x5),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x4,x2)),x3),x5))) ....... U1408 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), x4), equivalent_2(x0, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x2, x5), equivalent_2(x3, x5)), x1))))) ....... R4 [R3:L0, U1408:L0] % Derivation of unit clause U2681: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),equivalent_2(x2,x4)),x3))) ....... U388 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), x1)), equivalent_2(x0, equivalent_2(x2, x4))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U388:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),x4),equivalent_2(x0,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x2,x5),equivalent_2(x3,x5)),x1))))) ....... U2210 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, equivalent_2(x3, x4)), equivalent_2(equivalent_2(equivalent_2(x1, x5), equivalent_2(x2, x5)), equivalent_2(equivalent_2(x3, x6), equivalent_2(x4, x6)))))) ....... R4 [R3:L0, U2210:L0] % Derivation of unit clause U3965: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x1,x3)))) ....... U519 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4))), equivalent_2(x5, x1)), equivalent_2(x0, x5)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U519:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,equivalent_2(x3,x4)),equivalent_2(equivalent_2(equivalent_2(x1,x5),equivalent_2(x2,x5)),equivalent_2(equivalent_2(x3,x6),equivalent_2(x4,x6)))))) ....... U2681 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4))), equivalent_2(x5, x1)), equivalent_2(x6, x7)), equivalent_2(equivalent_2(equivalent_2(x0, x8), equivalent_2(x5, x8)), equivalent_2(equivalent_2(x6, x9), equivalent_2(x7, x9))))) ....... R4 [R3:L0, U2681:L0] % Derivation of unit clause U4698: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x4),equivalent_2(x0,x4))) ....... U521 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x0), x1)) | is_a_theorem_1(x1) ....... R3 [R2:L0, U521:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)),equivalent_2(x2,x4))),equivalent_2(x5,x1)),equivalent_2(x6,x7)),equivalent_2(equivalent_2(equivalent_2(x0,x8),equivalent_2(x5,x8)),equivalent_2(equivalent_2(x6,x9),equivalent_2(x7,x9))))) ....... U3965 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x3), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), x7), equivalent_2(equivalent_2(x2, x3), x7)))) ....... R4 [R3:L0, U3965:L0] % Derivation of unit clause U12468: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(x1,x1)))) ....... U804 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), equivalent_2(x4, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U804:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x3),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),x7),equivalent_2(equivalent_2(x2,x3),x7)))) ....... U4698 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x4), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, x6)), equivalent_2(x5, x7))), x8), equivalent_2(equivalent_2(x0, x4), x8))) ....... R4 [R3:L0, U4698:L0] % Derivation of unit clause U14456: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x0)) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3))), x0), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x6),equivalent_2(x1,x6)),x2),equivalent_2(x3,x5)))) ....... U806 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), x2)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), equivalent_2(x0, x3)), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U806:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))),x4),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7))),x8),equivalent_2(equivalent_2(x0,x4),x8))) ....... U12468 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x1), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)))), equivalent_2(x0, x2))) ....... R4 [R3:L0, U12468:L0] % Derivation of unit clause U17457: % ~is_a_theorem_1(equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0()))))))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x4,x4)),equivalent_2(x1,x3)))) ....... U1455 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x3, x2)), equivalent_2(x4, x4)), equivalent_2(x1, x3))), equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0()))))))) ....... R2 [R1:L0, U1455:L0] % Derivation of the empty clause: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x3,x2)),equivalent_2(x4,x4)),equivalent_2(x1,x3))),equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0()))))))) ....... U17457 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)))),equivalent_2(x0,x2))) ....... U14456 % [] ....... R1 [U17457:L0, U14456:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 185345 % resolvents: 185336 factors: 9 % Number of unit clauses generated: 165361 % % unit clauses generated to total clauses generated: 89.22 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 126 [4] = 17330 % Total = 17458 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 165361 [2] = 19971 [3] = 13 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)5314 (-)12144 % ------------------ % Total: (+)5314 (-)12144 % Total number of unit clauses retained: 17458 % Number of clauses skipped because of their length: 106 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 185439 % Number of unification failures: 29066 % Number of unit to unit unification failures: 64531716 % 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: 147445 % N unit clauses dropped because too much nesting: 4333 % 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: 12 % Number of states in UCFA table: 325469 % Total number of terms of all unit clauses in table: 881194 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.62 % Ratio n states used/total unit clauses terms: 0.37 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 214505 % ConstructUnitClause() = 164901 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.89 secs % -------------------------------------------------------- % | | % Inferences per sec: 1333 % | | % -------------------------------------------------------- % Elapsed time: 142 secs % CPU time: 139.61 secs % %------------------------------------------------------------------------------