%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL107-1 : TPTP v5.0.0. Released v1.0.0. % Transfm : add_equality % Format : carine % Command : carine %s t=%d xo=off uct=32000 % Computer : art06.cs.miami.edu % Model : i686 i686 % CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz % Memory : 2018MB % OS : Linux 2.6.26.8-57.fc8 % CPULimit : 300s % DateTime : Sun Nov 28 00:00:53 EST 2010 % Result : Unsatisfiable 2.53s % Output : Refutation 2.53s % 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/SystemOnTPTP23383/LCL/LCL107-1+noeq.car t=300 xo=off uct=32000 % CARINE version 0.734 (Dec 2003) % Initializing tables ... done. % Parsing ... done. % Calculating time slices ... done. % Building Lookup Tables ... done. % Looking for a proof at depth = 1 ... % t = 1 secs [nr = 3] [nf = 0] [nu = 0] [ut = 2] % Looking for a proof at depth = 2 ... % t = 1 secs [nr = 62] [nf = 0] [nu = 26] [ut = 19] % Looking for a proof at depth = 3 ... % t = 1 secs [nr = 150] [nf = 4] [nu = 73] [ut = 19] % 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(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) % B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) % Unit Clauses: % -------------- % U1: < d0 v14 dv7 f13 c0 t27 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) % U2: < d2 v14 dv7 f21 c8 t43 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) % U4: < d2 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3))) % U6: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) % U7: < d2 v18 dv9 f17 c0 t35 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) % U15: < d2 v20 dv10 f27 c8 t55 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(x9,x8),equivalent_2(x9,x7)),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) % U96: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5)) % U99: < d4 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) % U102: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) % U104: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3)))) % U106: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x3)),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7))),equivalent_2(x4,equivalent_2(x6,x7))),equivalent_2(equivalent_2(equivalent_2(x8,x0),equivalent_2(x8,x1)),equivalent_2(x2,x9)))),equivalent_2(x3,x9))) % U111: < d4 v8 dv4 f7 c0 t15 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2)))) % U116: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) % U118: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)))),equivalent_2(x2,equivalent_2(x3,equivalent_2(x5,x6)))))),equivalent_2(x1,x7)),x7)) % U458: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x1,equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)))),equivalent_2(x2,equivalent_2(x0,equivalent_2(x4,x5))))) % U2875: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x4))),equivalent_2(x0,equivalent_2(x3,x4)))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1 % Derivation of unit clause U2: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_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(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R1 [B0:L0, B2:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U4: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x1), equivalent_2(x2, x0)), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x6, x4), equivalent_2(x6, x5))), x3))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U6: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3))) ....... U4 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6))), equivalent_2(x3, equivalent_2(x5, x6))), x7)), equivalent_2(equivalent_2(x1, x2), x7))) ....... R2 [R1:L0, U4:L0] % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(equivalent_2(x8, x5), equivalent_2(x8, x6)), x7))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U15: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U2 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(), equivalent_2(a_0(), b_0())), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6)))), equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(equivalent_2(x9, x8), equivalent_2(x9, x7)), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, U2:L0] % Derivation of unit clause U96: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x1, equivalent_2(x3, x4))), x5), x5)) ....... R4 [R3:L0, U6:L0] % Derivation of unit clause U99: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5)) ....... U96 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2))) ....... R4 [R3:L0, U96:L0] % Derivation of unit clause U102: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U99 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x3, x4)))), x5), x5)) ....... R4 [R3:L0, U99:L0] % Derivation of unit clause U104: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) ....... U102 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x4)), x0), equivalent_2(x4, x3)))) ....... R4 [R3:L0, U102:L0] % Derivation of unit clause U106: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U6 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U6:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3)))) ....... U104 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x3)), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7))), equivalent_2(x4, equivalent_2(x6, x7))), equivalent_2(equivalent_2(equivalent_2(x8, x0), equivalent_2(x8, x1)), equivalent_2(x2, x9)))), equivalent_2(x3, x9))) ....... R4 [R3:L0, U104:L0] % Derivation of unit clause U111: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(x3, x1), equivalent_2(x3, x2)))) ....... R4 [R3:L0, U7:L0] % Derivation of unit clause U116: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) ....... U102 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x1, x3), x0), equivalent_2(x3, x2)))) ....... R4 [R3:L0, U102:L0] % Derivation of unit clause U118: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U7 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, x4)), equivalent_2(equivalent_2(x2, x3), x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x3)),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7))),equivalent_2(x4,equivalent_2(x6,x7))),equivalent_2(equivalent_2(equivalent_2(x8,x0),equivalent_2(x8,x1)),equivalent_2(x2,x9)))),equivalent_2(x3,x9))) ....... U106 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)))), equivalent_2(x2, equivalent_2(x3, equivalent_2(x5, x6)))))), equivalent_2(x1, x7)), x7)) ....... R4 [R3:L0, U106:L0] % Derivation of unit clause U458: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)))),equivalent_2(x2,equivalent_2(x3,equivalent_2(x5,x6)))))),equivalent_2(x1,x7)),x7)) ....... U118 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(equivalent_2(x4, x0), equivalent_2(x4, equivalent_2(x2, x3)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U118:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x1,x3),x0),equivalent_2(x3,x2)))) ....... U116 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x1, equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)))), equivalent_2(x2, equivalent_2(x0, equivalent_2(x4, x5))))) ....... R4 [R3:L0, U116:L0] % Derivation of unit clause U2875: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... 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(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x1,equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)))),equivalent_2(x2,equivalent_2(x0,equivalent_2(x4,x5))))) ....... U458 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x1), equivalent_2(x2, x0)), equivalent_2(x3, x4))), equivalent_2(equivalent_2(x5, x3), equivalent_2(x5, x4))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U458:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2)))) ....... U111 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x4))), equivalent_2(x0, equivalent_2(x3, x4)))) ....... R4 [R3:L0, U111:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x4))),equivalent_2(x0,equivalent_2(x3,x4)))) ....... U2875 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(c_0(),equivalent_2(a_0(),b_0())),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(equivalent_2(x9,x8),equivalent_2(x9,x7)),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))) ....... U15 % [] ....... R1 [U2875:L0, U15:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 17582 % resolvents: 17574 factors: 8 % Number of unit clauses generated: 17390 % % unit clauses generated to total clauses generated: 98.91 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 2 [2] = 17 [4] = 2857 % Total = 2876 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 17390 [2] = 181 [3] = 11 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)2365 (-)511 % ------------------ % Total: (+)2365 (-)511 % Total number of unit clauses retained: 2876 % Number of clauses skipped because of their length: 116 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 17632 % Number of unification failures: 41804 % Number of unit to unit unification failures: 1208008 % 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: 29 % N unit clauses dropped because they exceeded max values: 14374 % N unit clauses dropped because too much nesting: 28 % 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: 13 % Number of states in UCFA table: 56558 % Total number of terms of all unit clauses in table: 130756 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.11 % Ratio n states used/total unit clauses terms: 0.43 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 59436 % ConstructUnitClause() = 17248 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 0.13 secs % -------------------------------------------------------- % | | % Inferences per sec: 8791 % | | % -------------------------------------------------------- % Elapsed time: 3 secs % CPU time: 2.52 secs % %------------------------------------------------------------------------------