%------------------------------------------------------------------------------ % File : CARINE---0.734 % Problem : LCL103-1 : 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 00:00:22 EST 2010 % Result : Unsatisfiable 20.27s % Output : Refutation 20.27s % 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/SystemOnTPTP23091/LCL/LCL103-1+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 = 5] [nf = 0] [nu = 0] [ut = 3] % Looking for a proof at depth = 2 ... % t = 0 secs [nr = 1313] [nf = 0] [nu = 612] [ut = 396] % Looking for a proof at depth = 3 ... % t = 0 secs [nr = 3696] [nf = 7] [nu = 2285] [ut = 396] % 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(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())) % B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) % B2: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) % B3: ~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 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) % U2: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) % U6: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1))))) % U7: < d2 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4)))))) % U8: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x2,x5),x1)))))) % U9: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x2,x7),x4))))))) % U10: < d2 v14 dv7 f13 c0 t27 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1))))))) % U11: < d2 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x4,x7),equivalent_2(equivalent_2(x8,x2),equivalent_2(equivalent_2(x1,x8),x3)))))))) % U12: < d2 v18 dv9 f17 c0 t35 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x2,x8),x4)))))))) % U13: < d2 v16 dv8 f15 c0 t31 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x3,x7),x1)))))))) % U14: < d2 v20 dv10 f19 c0 t39 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x1,x9),x3))))))))) % U15: < d2 v20 dv10 f19 c0 t39 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x2,x9),x4))))))))) % U16: < d2 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),x1))))))))) % U17: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x5,x9),equivalent_2(equivalent_2(x10,x2),equivalent_2(equivalent_2(x1,x10),x3)))))))))) % U18: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x1,x10),x3)))))))))) % U19: < d2 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x2,x10),x4)))))))))) % U20: < d2 v20 dv10 f19 c0 t39 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x4,x9),x1)))))))))) % U31: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x3))) % U89: < d2 v22 dv11 f21 c0 t43 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x5,x10),x3))))))))) % U142: < d2 v24 dv12 f23 c0 t47 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),x5))))),equivalent_2(equivalent_2(equivalent_2(x6,x7),x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x6,x11),x5)))))))) % U193: < d2 v26 dv13 f25 c0 t51 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x6),x8))))))),equivalent_2(equivalent_2(x9,x1),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(x0,x12),x8))))))) % U240: < d2 v26 dv13 f25 c0 t51 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x7),x9)))))))),equivalent_2(equivalent_2(x10,x0),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(equivalent_2(x2,x1),x12),x9)))))) % U296: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x0,x4),x2))))) % U7709: < d4 v10 dv5 f17 c8 t35 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),x4))),equivalent_2(equivalent_2(x4,equivalent_2(x3,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())))) % U10110: < d4 v20 dv10 f27 c8 t55 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1)))),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(equivalent_2(x8,x7),x9))),equivalent_2(equivalent_2(x9,equivalent_2(x8,x6)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0()))))) % U11255: < d4 v18 dv9 f17 c0 t35 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),x6))))),equivalent_2(equivalent_2(x7,x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x3,x2)),x8),x6))))) % --------------- Start of Proof --------------- % Derivation of unit clause U1: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1 % Derivation of unit clause U2: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2 % Derivation of unit clause U6: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1))))) ....... R2 [R1:L0, U1:L0] % Derivation of unit clause U7: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1))))) ....... U6 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x0, x5), equivalent_2(equivalent_2(x6, x3), equivalent_2(equivalent_2(x2, x6), x4)))))) ....... R2 [R1:L0, U6:L0] % Derivation of unit clause U8: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4)))))) ....... U7 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x2, x5), x1)))))) ....... R2 [R1:L0, U7:L0] % Derivation of unit clause U9: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x2,x5),x1)))))) ....... U8 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x0, x6), equivalent_2(equivalent_2(x7, x3), equivalent_2(equivalent_2(x2, x7), x4))))))) ....... R2 [R1:L0, U8:L0] % Derivation of unit clause U10: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x2,x7),x4))))))) ....... U9 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(x3, x4), x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x3, x6), x1))))))) ....... R2 [R1:L0, U9:L0] % Derivation of unit clause U11: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1))))))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x4, x7), equivalent_2(equivalent_2(x8, x2), equivalent_2(equivalent_2(x1, x8), x3)))))))) ....... R2 [R1:L0, U10:L0] % Derivation of unit clause U12: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x4,x7),equivalent_2(equivalent_2(x8,x2),equivalent_2(equivalent_2(x1,x8),x3)))))))) ....... U11 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x0, x6), equivalent_2(equivalent_2(x7, x3), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x2, x8), x4)))))))) ....... R2 [R1:L0, U11:L0] % Derivation of unit clause U13: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x0,x6),equivalent_2(equivalent_2(x7,x3),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x2,x8),x4)))))))) ....... U12 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(x3, x4), x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x3, x7), x1)))))))) ....... R2 [R1:L0, U12:L0] % Derivation of unit clause U14: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x3,x7),x1)))))))) ....... U13 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), equivalent_2(equivalent_2(x9, x2), equivalent_2(equivalent_2(x1, x9), x3))))))))) ....... R2 [R1:L0, U13:L0] % Derivation of unit clause U15: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x1,x9),x3))))))))) ....... U14 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x0, x7), equivalent_2(equivalent_2(x8, x3), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x2, x9), x4))))))))) ....... R2 [R1:L0, U14:L0] % Derivation of unit clause U16: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x2,x9),x4))))))))) ....... U15 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), x3), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), x1))))))))) ....... R2 [R1:L0, U15:L0] % Derivation of unit clause U17: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),x1))))))))) ....... U16 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(x4, x0), equivalent_2(equivalent_2(equivalent_2(x5, x6), x4), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x5, x9), equivalent_2(equivalent_2(x10, x2), equivalent_2(equivalent_2(x1, x10), x3)))))))))) ....... R2 [R1:L0, U16:L0] % Derivation of unit clause U18: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x5,x9),equivalent_2(equivalent_2(x10,x2),equivalent_2(equivalent_2(x1,x10),x3)))))))))) ....... U17 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), x0), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x4, x8), equivalent_2(equivalent_2(x9, x2), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x1, x10), x3)))))))))) ....... R2 [R1:L0, U17:L0] % Derivation of unit clause U19: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),x0),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x4,x8),equivalent_2(equivalent_2(x9,x2),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x1,x10),x3)))))))))) ....... U18 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), x4)), equivalent_2(equivalent_2(x5, x1), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x0, x7), equivalent_2(equivalent_2(x8, x3), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x2, x10), x4)))))))))) ....... R2 [R1:L0, U18:L0] % Derivation of unit clause U20: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x0,x7),equivalent_2(equivalent_2(x8,x3),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x2,x10),x4)))))))))) ....... U19 % is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(equivalent_2(x4, x5), x3), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x4, x9), x1)))))))))) ....... R2 [R1:L0, U19:L0] % Derivation of unit clause U31: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))) ....... R1 [B1:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(x2, x1), x0), x3))) ....... R2 [R1:L0, U2:L0] % Derivation of unit clause U89: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(equivalent_2(x4,x5),x3),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x4,x9),x1)))))))))) ....... U20 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x3))), equivalent_2(equivalent_2(x4, x0), equivalent_2(equivalent_2(equivalent_2(x5, x6), x4), equivalent_2(equivalent_2(x7, x6), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x5, x10), x3))))))))) ....... R2 [R1:L0, U20:L0] % Derivation of unit clause U142: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(equivalent_2(x4,x0),equivalent_2(equivalent_2(equivalent_2(x5,x6),x4),equivalent_2(equivalent_2(x7,x6),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x5,x10),x3))))))))) ....... U89 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x3), x5))))), equivalent_2(equivalent_2(equivalent_2(x6, x7), x0), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(x9, x8), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x6, x11), x5)))))))) ....... R2 [R1:L0, U89:L0] % Derivation of unit clause U193: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),x5))))),equivalent_2(equivalent_2(equivalent_2(x6,x7),x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(x9,x8),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x6,x11),x5)))))))) ....... U142 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x2), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x6), x8))))))), equivalent_2(equivalent_2(x9, x1), equivalent_2(equivalent_2(x10, x9), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x12, x11), equivalent_2(equivalent_2(x0, x12), x8))))))) ....... R2 [R1:L0, U142:L0] % Derivation of unit clause U240: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x2),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x6),x8))))))),equivalent_2(equivalent_2(x9,x1),equivalent_2(equivalent_2(x10,x9),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(x0,x12),x8))))))) ....... U193 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x5), equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x7), x9)))))))), equivalent_2(equivalent_2(x10, x0), equivalent_2(equivalent_2(x11, x10), equivalent_2(equivalent_2(x12, x11), equivalent_2(equivalent_2(equivalent_2(x2, x1), x12), x9)))))) ....... R2 [R1:L0, U193:L0] % Derivation of unit clause U296: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... B2 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x0), x2))) | is_a_theorem_1(x2) ....... R1 [B2:L0, B3:L1] % is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(x3,x4),x2),equivalent_2(equivalent_2(x5,x4),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x3,x6),x1))))))) ....... U10 % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x0, x4), x2))))) ....... R2 [R1:L0, U10:L0] % Derivation of unit clause U7709: % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())) ....... B0 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0()))) ....... R1 [B0:L0, B3:L2] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R2 [R1:L1, B3:L2] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x0,x4),x2))))) ....... U296 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x1, x5), x3)))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R3 [R2:L0, U296:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(x2,x1),x0),x3))) ....... U31 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(x3, x2), x4))), equivalent_2(equivalent_2(x4, equivalent_2(x3, x1)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0())))) ....... R4 [R3:L1, U31:L0] % Derivation of unit clause U10110: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U1 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1)))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U1:L0] % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(x3,x2),x4))),equivalent_2(equivalent_2(x4,equivalent_2(x3,x1)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0())))) ....... U7709 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x2, x4), x1)))), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x7, x5), equivalent_2(equivalent_2(x8, x7), x9))), equivalent_2(equivalent_2(x9, equivalent_2(x8, x6)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(a_0(), c_0())), equivalent_2(b_0(), c_0())), e_0()), e_0()))))) ....... R4 [R3:L1, U7709:L0] % Derivation of unit clause U11255: % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... B1 % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0] % ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2))), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0] % is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),x4)),equivalent_2(equivalent_2(x5,x1),equivalent_2(equivalent_2(x0,x5),equivalent_2(equivalent_2(x6,x3),equivalent_2(equivalent_2(x2,x6),x4)))))) ....... U7 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x3), x0), equivalent_2(equivalent_2(x4, x3), equivalent_2(equivalent_2(x5, x4), equivalent_2(equivalent_2(x2, x5), x1))))), x6)) | is_a_theorem_1(x6) ....... R3 [R2:L0, U7:L0] % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x5),equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x7),x9)))))))),equivalent_2(equivalent_2(x10,x0),equivalent_2(equivalent_2(x11,x10),equivalent_2(equivalent_2(x12,x11),equivalent_2(equivalent_2(equivalent_2(x2,x1),x12),x9)))))) ....... U240 % is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x4), x6))))), equivalent_2(equivalent_2(x7, x0), equivalent_2(equivalent_2(x8, x7), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x3, x2)), x8), x6))))) ....... R4 [R3:L0, U240:L0] % Derivation of the empty clause: % is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x4),x6))))),equivalent_2(equivalent_2(x7,x0),equivalent_2(equivalent_2(x8,x7),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x3,x2)),x8),x6))))) ....... U11255 % ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x3),x0),equivalent_2(equivalent_2(x4,x3),equivalent_2(equivalent_2(x2,x4),x1)))),equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x7,x5),equivalent_2(equivalent_2(x8,x7),x9))),equivalent_2(equivalent_2(x9,equivalent_2(x8,x6)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(a_0(),c_0())),equivalent_2(b_0(),c_0())),e_0()),e_0()))))) ....... U10110 % [] ....... R1 [U11255:L0, U10110:L0] % --------------- End of Proof --------------- % PROOF FOUND! % --------------------------------------------- % | Statistics | % --------------------------------------------- % Profile 3: Performance Statistics: % ================================== % Total number of generated clauses: 358035 % resolvents: 358024 factors: 11 % Number of unit clauses generated: 355341 % % unit clauses generated to total clauses generated: 99.25 % Number of unit clauses constructed and retained at depth [x]: % ============================================================= % [0] = 3 [2] = 393 [4] = 10860 % Total = 11256 % Number of generated clauses having [x] literals: % ------------------------------------------------ % [1] = 355341 [2] = 2677 [3] = 17 % Average size of a generated clause: 2.0 % Number of unit clauses per predicate list: % ========================================== % [0] is_a_theorem_1 (+)918 (-)10338 % ------------------ % Total: (+)918 (-)10338 % Total number of unit clauses retained: 11256 % Number of clauses skipped because of their length: 1289 % N base clauses skippped in resolve-with-all-base-clauses % because of the shortest resolvents table: 0 % Number of successful unifications: 358089 % Number of unification failures: 436592 % Number of unit to unit unification failures: 9489583 % N literal unification failure due to lookup root_id table: 35 % 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: 24 % N unit clauses dropped because they exceeded max values: 332912 % N unit clauses dropped because too much nesting: 95850 % 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: 232089 % Total number of terms of all unit clauses in table: 607756 % Max allowed number of states in UCFA: 528000 % Ratio n states used/total allowed states: 0.44 % Ratio n states used/total unit clauses terms: 0.38 % Number of symbols (columns) in UCFA: 40 % Profile 2: Number of calls to: % ============================== % PTUnify() = 794681 % ConstructUnitClause() = 344165 % Profile 1: Time spent in: % ========================= % ConstructUnitClause() : 1.52 secs % -------------------------------------------------------- % | | % Inferences per sec: 17902 % | | % -------------------------------------------------------- % Elapsed time: 21 secs % CPU time: 20.24 secs % %------------------------------------------------------------------------------