%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL018-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art11.cs.miami.edu % Model : i686 i686 % CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz % Memory : 2006MB % OS : Linux 2.6.31.5-127.fc12.i686.PAE % CPULimit : 300s % DateTime : Sat Nov 27 23:22:39 EST 2010 % Result : Unsatisfiable 82.80s % Output : Refutation 82.80s % 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/SystemOnTPTP15063/LCL/LCL018-1+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 = 92] [nf = 0] [nu = 45] [ut = 32] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 214] [nf = 4] [nu = 115] [ut = 32] % Looking for a proof at depth = 4 ... % +================================================+ % | | % | Congratulations!!! ........ A proof was found. | % | | % +================================================+ % Base Clauses and Unit Clauses used in proof: % ============================================ % Base Clauses: % ------------- % B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U0: < d0 v0 dv0 f5 c6 t11 td5 b nc > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) % U1: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) % U4: < d2 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) % U5: < d2 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) % U6: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) % U7: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) % U8: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5))) % U17: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3))))) % U18: < d2 v12 dv6 f11 c0 t23 td11 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,equivalent_2(equivalent_2(x3,equivalent_2(x5,x2)),x5))),x4))),x1))) % U216: < d4 v10 dv5 f9 c0 t19 td9 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1))) % U218: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6))) % U219: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)))) % U221: < d4 v14 dv7 f13 c0 t27 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) % U628: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x3,equivalent_2(equivalent_2(x6,equivalent_2(x7,x5)),x7))))),x4))) % U790: < d4 v14 dv7 f13 c0 t27 td9 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3)),x0),equivalent_2(equivalent_2(x2,equivalent_2(x6,x1)),x6))))) % U1001: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4)),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),x6),equivalent_2(x7,x5))),x0)) % U1004: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(x6,equivalent_2(x8,x5)),x8))),x7))),x4)) % U1218: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) % U1900: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5))))) % U2362: < d4 v8 dv4 f7 c0 t15 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) % U2498: < d4 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x5),x7)))),equivalent_2(equivalent_2(x1,equivalent_2(x8,x0)),x8)))) % U2506: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5)))),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x8),x7)),equivalent_2(x9,x8)),x9))) % U2859: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x0),x2),x1))) % U2860: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1))) % U2861: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) % U2863: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5))) % U2876: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2)))) % U2884: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0)) % U2889: < d4 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2)),equivalent_2(x4,x0)),x4))) % U2892: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5)))),x3)) % U2894: < d4 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1))) % U2895: < d4 v2 dv1 f1 c0 t3 td2 > is_a_theorem_1(equivalent_2(x0,x0)) % U3548: < d4 v12 dv6 f11 c0 t23 td10 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4),equivalent_2(x5,x0)),x5))) % U3975: < d4 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5))),x0)) % U4054: < d4 v12 dv6 f17 c6 t35 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))) % U4263: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(equivalent_2(x8,x6),x5),x8))),x7))),x4)) % U4675: < d4 v20 dv10 f25 c6 t51 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x1),x0),x3))),x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),x6),equivalent_2(x8,x7)),equivalent_2(equivalent_2(x5,equivalent_2(x9,x4)),x9))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))))) % U5237: < d4 v6 dv3 f5 c0 t11 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)))) % U5398: < d4 v26 dv13 f31 c6 t63 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),x9),equivalent_2(x11,x10)),equivalent_2(equivalent_2(x8,equivalent_2(x12,x7)),x12))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))))) % U19296: < d4 v16 dv8 f15 c0 t31 td11 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x7,x3),x2),x7)))),x0),x1))) % --------------- Start of Proof --------------- % Derivation of unit clause U0: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) ....... U0 % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2)))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U5: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2))), x1))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U6: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x0)) ....... R2 [R1:L0, U5:L0] % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5)))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(x4, equivalent_2(x6, x3)), x6))), x5))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U17: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(x0, equivalent_2(x1, x2)), x1)) | is_a_theorem_1(equivalent_2(x2, x0)) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x0)), x2), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3))))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U18: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(x0, equivalent_2(x1, x2)), x1)) | is_a_theorem_1(equivalent_2(x2, x0)) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5))) ....... U8 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, equivalent_2(equivalent_2(x3, equivalent_2(x5, x2)), x5))), x4))), x1))) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U216: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x3), x2), x4)))), x1))) ....... R4 [R3:L0, U4:L0] % Derivation of unit clause U218: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x3), x5), x4)), equivalent_2(x6, x5)), x6))) ....... R4 [R3:L0, U7:L0] % Derivation of unit clause U219: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3))))) ....... U17 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4)))) ....... R4 [R3:L0, U17:L0] % Derivation of unit clause U221: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1))) ....... U216 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x2), x1), x3)))), equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x5), x4), x6)))), x0)) ....... R4 [R3:L0, U216:L0] % Derivation of unit clause U628: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(x4,equivalent_2(x6,x3)),x6))),x5))) ....... U8 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x1, equivalent_2(x3, x0)), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U8:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(x3, equivalent_2(equivalent_2(x6, equivalent_2(x7, x5)), x7))))), x4))) ....... R4 [R3:L0, U7:L0] % Derivation of unit clause U790: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x0)),x2),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3))))) ....... U17 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x1, equivalent_2(x3, x0)), x3))), x2), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U17:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3)), x0), equivalent_2(equivalent_2(x2, equivalent_2(x6, x1)), x6))))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U1001: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6))) ....... U218 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U218:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x3), x2)), equivalent_2(x4, x3)), x4)), equivalent_2(equivalent_2(equivalent_2(x5, equivalent_2(x6, x7)), x6), equivalent_2(x7, x5))), x0)) ....... R4 [R3:L0, U5:L0] % Derivation of unit clause U1004: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x5),x4)),equivalent_2(x6,x5)),x6))) ....... U218 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U218:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,equivalent_2(equivalent_2(x3,equivalent_2(x5,x2)),x5))),x4))),x1))) ....... U18 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, equivalent_2(equivalent_2(x6, equivalent_2(x8, x5)), x8))), x7))), x4)) ....... R4 [R3:L0, U18:L0] % Derivation of unit clause U1218: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)))) ....... U219 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U219:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x3),x2),x4)))),x1))) ....... U216 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x5), x4), x6)))), x0)) ....... R4 [R3:L0, U216:L0] % Derivation of unit clause U1900: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x3,equivalent_2(equivalent_2(x6,equivalent_2(x7,x5)),x7))))),x4))) ....... U628 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x0, equivalent_2(equivalent_2(x3, equivalent_2(x4, x2)), x4))))), x1), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U628:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) ....... U221 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x4), x3), x5))))) ....... R4 [R3:L0, U221:L0] % Derivation of unit clause U2362: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x5),x4),x6)))),x0)) ....... U1218 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x5)), x4), equivalent_2(x5, x3)), x2)), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U1218:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4)),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),x6),equivalent_2(x7,x5))),x0)) ....... U1001 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x2), x1), x3))), x0)) ....... R4 [R3:L0, U1001:L0] % Derivation of unit clause U2498: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5))))) ....... U1900 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1900:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x5)),x4),equivalent_2(x5,x3)),x0),equivalent_2(equivalent_2(x2,equivalent_2(x6,x1)),x6))))) ....... U790 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(x5, equivalent_2(x6, equivalent_2(equivalent_2(equivalent_2(x7, x6), x5), x7)))), equivalent_2(equivalent_2(x1, equivalent_2(x8, x0)), x8)))) ....... R4 [R3:L0, U790:L0] % Derivation of unit clause U2506: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5))))) ....... U1900 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x2))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U1900:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x5),x7)))),equivalent_2(equivalent_2(x1,equivalent_2(x8,x0)),x8)))) ....... U2498 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x4), x3), x5)))), equivalent_2(equivalent_2(equivalent_2(x6, equivalent_2(equivalent_2(equivalent_2(x7, x6), x8), x7)), equivalent_2(x9, x8)), x9))) ....... R4 [R3:L0, U2498:L0] % Derivation of unit clause U2859: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0))) ....... U1 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x0), x2), x1))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U2860: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x2)))) ....... U4 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3))), x1))) ....... R4 [R3:L0, U4:L0] % Derivation of unit clause U2861: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2))),x1))) ....... U5 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), x1), equivalent_2(x3, x2))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4))), x0)) ....... R4 [R3:L0, U5:L0] % Derivation of unit clause U2863: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,equivalent_2(x3,x4)),x3),equivalent_2(x4,x2)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x4), x3), x6))), x5))) ....... R4 [R3:L0, U7:L0] % Derivation of unit clause U2876: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(x6,equivalent_2(x8,x5)),x8))),x7))),x4)) ....... U1004 % is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x0, equivalent_2(x2, x1)), x2)))) ....... R4 [R3:L0, U1004:L0] % Derivation of unit clause U2884: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x0),x2),x1))) ....... U2859 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3))), x1), x0)) ....... R4 [R3:L0, U2859:L0] % Derivation of unit clause U2889: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2)))) ....... U2876 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), x1), equivalent_2(x3, x2)), equivalent_2(x4, x0)), x4))) ....... R4 [R3:L0, U2876:L0] % Derivation of unit clause U2892: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2)),equivalent_2(x4,x0)),x4))) ....... U2889 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5)))), x3)) ....... R4 [R3:L0, U2889:L0] % Derivation of unit clause U2894: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5)))),x3)) ....... U2892 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1))) ....... R4 [R3:L0, U2892:L0] % Derivation of unit clause U2895: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x2),x1),x3))),x0)) ....... U2362 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2362:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1))) ....... U2894 % is_a_theorem_1(equivalent_2(x0, x0)) ....... R4 [R3:L0, U2894:L0] % Derivation of unit clause U3548: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x4),x3),x5)))),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(x7,x6),x8),x7)),equivalent_2(x9,x8)),x9))) ....... U2506 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2506:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x0,equivalent_2(x2,x1)),x2)))) ....... U2876 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x1), x3), x2)), equivalent_2(x4, x3)), x4), equivalent_2(x5, x0)), x5))) ....... R4 [R3:L0, U2876:L0] % Derivation of unit clause U3975: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1))) ....... U2860 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5))), x0), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U2860:L0] % is_a_theorem_1(equivalent_2(x0,x0)) ....... U2895 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x2), equivalent_2(x3, x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), x6), x4), equivalent_2(x6, x5))), x0)) ....... R4 [R3:L0, U2895:L0] % Derivation of unit clause U4054: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),x1),equivalent_2(x3,x2))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4))),x0)) ....... U2861 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U2861:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))) ....... U0 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x2), equivalent_2(x4, x3)), equivalent_2(equivalent_2(x1, equivalent_2(x5, x0)), x5))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0())))) ....... R4 [R3:L1, U0:L0] % Derivation of unit clause U4263: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5))) ....... U2863 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2863:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x1),x3),x2)),equivalent_2(x4,x3)),x4),equivalent_2(x5,x0)),x5))) ....... U3548 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), x1)), equivalent_2(x3, x2)), x3), equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, equivalent_2(equivalent_2(equivalent_2(x8, x6), x5), x8))), x7))), x4)) ....... R4 [R3:L0, U3548:L0] % Derivation of unit clause U4675: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5))) ....... U2863 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2863:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3)),equivalent_2(equivalent_2(x1,equivalent_2(x5,x0)),x5))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))) ....... U4054 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(x3, x1), x0), x3))), x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6, x7), x8), x6), equivalent_2(x8, x7)), equivalent_2(equivalent_2(x5, equivalent_2(x9, x4)), x9))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0()))))) ....... R4 [R3:L1, U4054:L0] % Derivation of unit clause U5237: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0)) ....... U2884 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2884:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x0),x2),x1)),equivalent_2(x3,x2)),x3),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,equivalent_2(equivalent_2(equivalent_2(x8,x6),x5),x8))),x7))),x4)) ....... U4263 % is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2)))) ....... R4 [R3:L0, U4263:L0] % Derivation of unit clause U5398: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x2),equivalent_2(x4,x3))),x1),x0)) ....... U2884 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2884:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(equivalent_2(x3,x1),x0),x3))),x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),x6),equivalent_2(x8,x7)),equivalent_2(equivalent_2(x5,equivalent_2(x9,x4)),x9))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0()))))) ....... U4675 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x2, x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(x6, x4), x3), x6))), x5), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), x11), x9), equivalent_2(x11, x10)), equivalent_2(equivalent_2(x8, equivalent_2(x12, x7)), x12))), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(b_0(), c_0())), c_0()), equivalent_2(b_0(), a_0())))))) ....... R4 [R3:L1, U4675:L0] % Derivation of unit clause U19296: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x1),equivalent_2(x2,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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | is_a_theorem_1(x3) ....... 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(equivalent_2(x0, equivalent_2(x1, x2)), x1), equivalent_2(x2, x0)), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x2),equivalent_2(x3,x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),x6),x4),equivalent_2(x6,x5))),x0)) ....... U3975 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, equivalent_2(x3, x4)), x3), equivalent_2(x4, x2)), equivalent_2(equivalent_2(equivalent_2(x5, x1), x0), x5))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U3975:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)))) ....... U5237 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, x6)), x5), equivalent_2(x6, x4)), equivalent_2(equivalent_2(equivalent_2(x7, x3), x2), x7)))), x0), x1))) ....... R4 [R3:L0, U5237:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,x6)),x5),equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x7,x3),x2),x7)))),x0),x1))) ....... U19296 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x2,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(x6,x4),x3),x6))),x5),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),x9),equivalent_2(x11,x10)),equivalent_2(equivalent_2(x8,equivalent_2(x12,x7)),x12))),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(b_0(),c_0())),c_0()),equivalent_2(b_0(),a_0())))))) ....... U5398 % [] ....... R1 [U19296:L0, U5398:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 409836 % resolvents: 409828 factors: 8 % Number of unit clauses generated: 409609 % % unit clauses generated to total clauses generated: 99.94 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 30 [4] = 19265 % Total = 19297 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 409609 [2] = 216 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)3105 (-)16192 % ------------------ % Total: (+)3105 (-)16192 % Total number of unit clauses retained: 19297 % Number of clauses skipped because of their length: 129 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 409974 % Number of unification failures: 43193 % Number of unit to unit unification failures: 50265028 % N literal unification failure due to lookup root_id table: 26 % N base clause resolution failure due to lookup table: 0 % N UC-BCL resolution dropped due to lookup table: 0 % Max entries in substitution set: 22 % N unit clauses dropped because they exceeded max values: 390017 % N unit clauses dropped because too much nesting: 63997 % 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: 327112 % Total number of terms of all unit clauses in table: 1031435 % 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: 0.32 % Number of symbols (columns) in UCFA: 39 % Profile 2: Number of calls to: % ============================== % PTUnify() = 453167 % ConstructUnitClause() = 409312 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 1.93 secs % -------------------------------------------------------- % | | % Inferences per sec: 4998 % | | % -------------------------------------------------------- % Elapsed time: 84 secs % CPU time: 82.79 secs % %------------------------------------------------------------------------------