%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL128-1 : 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 00:07:58 EST 2010 % Result : Unsatisfiable 28.44s % Output : Refutation 28.44s % 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/SystemOnTPTP25558/LCL/LCL128-1+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 = 48] [nf = 0] [nu = 18] [ut = 14] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 111] [nf = 5] [nu = 46] [ut = 14] % 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(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(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) % 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(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) % U3: < d2 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) % U4: < 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))) % U7: < d2 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(x9,x8)),equivalent_2(x7,x9)))) % U8: < 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)))) % U21: < d4 v4 dv2 f11 c8 t23 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),equivalent_2(equivalent_2(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())))),x0),x1))) % U58: < d4 v10 dv5 f9 c0 t19 td7 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)),equivalent_2(x2,x4)),x1)))) % U59: < d4 v22 dv11 f21 c0 t43 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),x7),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x8,x9),equivalent_2(x10,x9)),equivalent_2(x8,x10)),x7))) % U67: < d4 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)),x3))) % U143: < d4 v24 dv12 f23 c0 t47 td7 > 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) % U195: < d4 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2)),equivalent_2(x3,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7)),x4))))) % U223: < d4 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),x7),equivalent_2(equivalent_2(x4,x6),x7)))) % U224: < 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)))) % U237: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0)) % U273: < d4 v6 dv3 f13 c8 t27 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2))) % U397: < d4 v8 dv4 f15 c8 t31 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2),x3))) % U478: < d4 v10 dv5 f17 c8 t35 td11 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),x3),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2),x3),x4))) % U574: < d4 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))) % U620: < d4 v24 dv12 f23 c0 t47 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) % U657: < d4 v30 dv15 f29 c0 t59 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11))),equivalent_2(equivalent_2(equivalent_2(x12,x13),equivalent_2(x14,x13)),equivalent_2(x12,x14)))) % U813: < d4 v8 dv4 f15 c8 t31 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),equivalent_2(x3,x2)),equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x3))) % U907: < d4 v6 dv3 f13 c8 t27 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(x1,x0)),x2),equivalent_2(equivalent_2(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())))),x1),x2))) % U949: < d4 v4 dv2 f11 c8 t23 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))),x0)),equivalent_2(a_0(),x1))) % U1190: < d4 v26 dv13 f25 c0 t51 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),x12),equivalent_2(equivalent_2(x9,x11),x12)))) % U1298: < d4 v20 dv10 f19 c0 t39 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),equivalent_2(equivalent_2(x9,x7),x8)),equivalent_2(x6,x9)))) % U1330: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)),x2),x3)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x8),equivalent_2(equivalent_2(x1,x7),x8)))) % U1353: < d4 v12 dv6 f11 c0 t23 td8 > 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),x5),equivalent_2(equivalent_2(x0,x4),x5))) % U1596: < d4 v6 dv3 f13 c8 t27 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))),x0)),x2),equivalent_2(equivalent_2(a_0(),x1),x2))) % U2264: < d4 v12 dv6 f11 c0 t23 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(equivalent_2(x0,x5),equivalent_2(x4,x5)))) % U2427: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5))),x2)))) % U5841: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(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(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),x5)))) % U6684: < d4 v24 dv12 f23 c0 t47 td8 > 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(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7))),equivalent_2(equivalent_2(x0,x8),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11))),x8)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... U1 % Derivation of unit clause U3: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6)))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... B1 % ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(x9, x8)), equivalent_2(x7, x9)))) ....... R2 [R1:L0, U3:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... B1 % ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... 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))) ....... U4 % 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, U4:L0] % Derivation of unit clause U21: % ~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(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~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()))))))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, x0)) ....... R2 [R1:L0, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(a_0(), x1), equivalent_2(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())))), x1)))) ....... R3 [R2:L0, U4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), x1), equivalent_2(equivalent_2(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())))), x0), x1))) ....... R4 [R3:L1, U4:L0] % Derivation of unit clause U58: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), x7)) | is_a_theorem_1(x7) ....... 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))) ....... U4 % is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4)), x1)))) ....... R4 [R3:L0, U4:L0] % Derivation of unit clause U59: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U1:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)),equivalent_2(x2,x4)),x1)))) ....... U58 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6))), x7), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x8, x9), equivalent_2(x10, x9)), equivalent_2(x8, x10)), x7))) ....... R4 [R3:L0, U58:L0] % Derivation of unit clause U67: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U3:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x4,x3)),equivalent_2(x2,x4)),x1)))) ....... U58 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6)), x3))) ....... R4 [R3:L0, U58:L0] % Derivation of unit clause U143: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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)),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)),x3))) ....... U67 % ~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(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8)))), x9)) | is_a_theorem_1(x9) ....... R3 [R2:L0, U67:L0] % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8)))), equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x11, x10)), equivalent_2(x9, x11)))) ....... R4 [R3:L0, U1:L0] % Derivation of unit clause U195: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),x7),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x8,x9),equivalent_2(x10,x9)),equivalent_2(x8,x10)),x7))) ....... U59 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, x6)), equivalent_2(x5, x7)))), equivalent_2(equivalent_2(equivalent_2(x8, x9), equivalent_2(x10, x9)), equivalent_2(x8, x10))), x11))) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x12, x13), equivalent_2(x14, x13)), equivalent_2(x12, x14)), x11)) ....... R3 [R2:L1, U59:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), equivalent_2(x0, x2)), equivalent_2(x3, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x7, x6)), equivalent_2(x5, x7)), x4))))) ....... R4 [R3:L0, U3:L0] % Derivation of unit clause U223: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6))),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(x9,x8)),equivalent_2(x7,x9)))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), x7), equivalent_2(equivalent_2(x4, x6), x7)))) ....... R4 [R3:L0, U7:L0] % Derivation of unit clause U224: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % 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)))) ....... U8 % 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, U8:L0] % Derivation of unit clause U237: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2)),equivalent_2(x3,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7)),x4))))) ....... U195 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0)) ....... R4 [R3:L0, U195:L0] % Derivation of unit clause U273: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),equivalent_2(equivalent_2(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())))),x0),x1))) ....... U21 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), x1), x2), equivalent_2(equivalent_2(equivalent_2(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())))), x0), x1), x2))) ....... R4 [R3:L1, U21:L0] % Derivation of unit clause U397: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2))) ....... U273 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))), x0), x1), x2), x3))) ....... R4 [R3:L1, U273:L0] % Derivation of unit clause U478: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)))) ....... U3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U3:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2),x3))) ....... U397 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), x1), x2), x3), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))), x0), x1), x2), x3), x4))) ....... R4 [R3:L1, U397:L0] % Derivation of unit clause U574: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0)) ....... U237 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8)))) ....... R4 [R3:L0, U237:L0] % Derivation of unit clause U620: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))) ....... U574 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8))), equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x11, x10)), equivalent_2(x9, x11)))) ....... R4 [R3:L0, U574:L0] % Derivation of unit clause U657: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U620 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8))), equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x11, x10)), equivalent_2(x9, x11))), equivalent_2(equivalent_2(equivalent_2(x12, x13), equivalent_2(x14, x13)), equivalent_2(x12, x14)))) ....... R4 [R3:L0, U620:L0] % Derivation of unit clause U813: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),x3),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x2),x3),x4))) ....... U478 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), x1), x2), equivalent_2(x3, x2)), equivalent_2(equivalent_2(equivalent_2(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())))), x0), x1), x3))) ....... R4 [R3:L1, U478:L0] % Derivation of unit clause U907: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),x1),x2),equivalent_2(x3,x2)),equivalent_2(equivalent_2(equivalent_2(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())))),x0),x1),x3))) ....... U813 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), equivalent_2(x1, x0)), x2), equivalent_2(equivalent_2(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())))), x1), x2))) ....... R4 [R3:L1, U813:L0] % Derivation of unit clause U949: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x1)),equivalent_2(x0,x2))) ....... U4 % ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))) ....... R3 [R2:L0, U4:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(x1,x0)),x2),equivalent_2(equivalent_2(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())))),x1),x2))) ....... U907 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))), x0)), equivalent_2(a_0(), x1))) ....... R4 [R3:L1, U907:L0] % Derivation of unit clause U1190: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U143 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U143:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11))),equivalent_2(equivalent_2(equivalent_2(x12,x13),equivalent_2(x14,x13)),equivalent_2(x12,x14)))) ....... U657 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x11, x10)), x12), equivalent_2(equivalent_2(x9, x11), x12)))) ....... R4 [R3:L0, U657:L0] % Derivation of unit clause U1298: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U143 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U143:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),x12),equivalent_2(equivalent_2(x9,x11),x12)))) ....... U1190 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5)), x1), x2)), x0), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6, x7), x8), equivalent_2(equivalent_2(x9, x7), x8)), equivalent_2(x6, x9)))) ....... R4 [R3:L0, U1190:L0] % Derivation of unit clause U1330: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U143 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U143:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),x1),x2)),x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x6,x7),x8),equivalent_2(equivalent_2(x9,x7),x8)),equivalent_2(x6,x9)))) ....... U1298 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x6, x5)), equivalent_2(x4, x6)), x2), x3)), equivalent_2(equivalent_2(equivalent_2(x0, x7), x8), equivalent_2(equivalent_2(x1, x7), x8)))) ....... R4 [R3:L0, U1298:L0] % Derivation of unit clause U1353: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U143 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U143:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),equivalent_2(x4,x6)),x2),x3)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x8),equivalent_2(equivalent_2(x1,x7),x8)))) ....... U1330 % 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), x5), equivalent_2(equivalent_2(x0, x4), x5))) ....... R4 [R3:L0, U1330:L0] % Derivation of unit clause U1596: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8)))),equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11)))) ....... U143 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1))) | is_a_theorem_1(equivalent_2(x0, x2)) ....... R3 [R2:L0, U143:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))),x0)),equivalent_2(a_0(),x1))) ....... U949 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), x0), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))), x0)), x2), equivalent_2(equivalent_2(a_0(), x1), x2))) ....... R4 [R3:L1, U949:L0] % Derivation of unit clause U2264: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),x7),equivalent_2(equivalent_2(x4,x6),x7)))) ....... U223 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(x0, x2), x3)) ....... R3 [R2:L0, U223:L0] % 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),x5),equivalent_2(equivalent_2(x0,x4),x5))) ....... U1353 % 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(equivalent_2(x0, x5), equivalent_2(x4, x5)))) ....... R4 [R3:L0, U1353:L0] % Derivation of unit clause U2427: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x6,x5)),x7),equivalent_2(equivalent_2(x4,x6),x7)))) ....... U223 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x1)), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(x0, x2), x3)) ....... R3 [R2:L0, U223: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(equivalent_2(x0,x5),equivalent_2(x4,x5)))) ....... U2264 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x4)), equivalent_2(x3, x5))), x2)))) ....... R4 [R3:L0, U2264:L0] % Derivation of unit clause U5841: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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)))) ....... U224 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4))), x1)) ....... R3 [R2:L0, U224:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x4)),equivalent_2(x3,x5))),x2)))) ....... U2427 % is_a_theorem_1(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(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(x8, x7)), equivalent_2(x6, x8))), x5)))) ....... R4 [R3:L0, U2427:L0] % Derivation of unit clause U6684: % is_a_theorem_1(equivalent_2(x0,equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,x2)),equivalent_2(x1,x3))))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), 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(x0, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, x2)), equivalent_2(x1, x3)))), equivalent_2(x4, x5))) | ~is_a_theorem_1(x4) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L1] % 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)))) ....... U224 % ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x4, x3)), equivalent_2(x2, x4))), x1)) ....... R3 [R2:L0, U224:L0] % is_a_theorem_1(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(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(x8,x7)),equivalent_2(x6,x8))),x5)))) ....... U5841 % 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(equivalent_2(x5, x6), equivalent_2(x7, x6)), equivalent_2(x5, x7))), equivalent_2(equivalent_2(x0, x8), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x11, x10)), equivalent_2(x9, x11))), x8)))) ....... R4 [R3:L0, U5841:L0] % Derivation of the empty clause: % 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(equivalent_2(x5,x6),equivalent_2(x7,x6)),equivalent_2(x5,x7))),equivalent_2(equivalent_2(x0,x8),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x11,x10)),equivalent_2(x9,x11))),x8)))) ....... U6684 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),x0),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))),x0)),x2),equivalent_2(equivalent_2(a_0(),x1),x2))) ....... U1596 % [] ....... R1 [U6684:L0, U1596:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 14665 % resolvents: 14656 factors: 9 % Number of unit clauses generated: 14296 % % unit clauses generated to total clauses generated: 97.48 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 12 [4] = 6671 % Total = 6685 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 14296 [2] = 357 [3] = 12 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)2762 (-)3923 % ------------------ % Total: (+)2762 (-)3923 % Total number of unit clauses retained: 6685 % Number of clauses skipped because of their length: 303 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 14781 % Number of unification failures: 19112 % Number of unit to unit unification failures: 10832501 % N literal unification failure due to lookup root_id table: 27 % 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: 20 % N unit clauses dropped because they exceeded max values: 7523 % N unit clauses dropped because too much nesting: 1076 % 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: 132080 % Total number of terms of all unit clauses in table: 344235 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.25 % Ratio n states used/total unit clauses terms: 0.38 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 33893 % ConstructUnitClause() = 14206 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.12 secs % -------------------------------------------------------- % | | % Inferences per sec: 524 % | | % -------------------------------------------------------- % Elapsed time: 29 secs % CPU time: 28.44 secs % %------------------------------------------------------------------------------