TSTP Solution File: LCL166-1 by CARINE---0.734
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL166-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art01.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 00:13:39 EST 2010
% Result : Unsatisfiable 34.47s
% Output : Refutation 34.47s
% 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/SystemOnTPTP13277/LCL/LCL166-1+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 = 40] [nf = 0] [nu = 17] [ut = 12]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 94] [nf = 5] [nu = 43] [ut = 12]
% 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(b_0(),equivalent_2(c_0(),a_0()))))
% B1: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))))
% U3: < d2 v10 dv5 f9 c0 t19 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)))
% U4: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2))
% U8: < d2 v14 dv7 f13 c0 t27 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))),x2))),x0)))
% U9: < d2 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x4)),x0)))
% U16: < d4 v12 dv6 f17 c6 t35 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),x3)),x5)))
% U59: < d4 v16 dv8 f15 c0 t31 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x1),x2)))),x4),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),equivalent_2(x4,x0)))
% U106: < d4 v12 dv6 f17 c6 t35 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),x5),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x5,x3))))
% U159: < d4 v22 dv11 f21 c0 t43 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x1),x2)))),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x7),x5)),equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9)))),x7)),equivalent_2(x4,x0)))
% U160: < d4 v24 dv12 f23 c0 t47 td9 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x3),x1)),equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))),x3)),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x0),x7)),equivalent_2(x9,equivalent_2(equivalent_2(x10,x11),equivalent_2(equivalent_2(x11,x9),x10))))))
% U171: < d4 v18 dv9 f17 c0 t35 td11 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))))),x3)),x5)))
% U179: < d4 v12 dv6 f11 c0 t23 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),x2))
% U181: < d4 v16 dv8 f15 c0 t31 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))))
% U225: < d4 v24 dv12 f29 c6 t59 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),equivalent_2(x10,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x11,x9)))))
% U342: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))))
% U361: < d4 v14 dv7 f13 c0 t27 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),x3),x2),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5))))))
% U376: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),x5),x4),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))),x0)))
% U420: < d4 v16 dv8 f15 c0 t31 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3))),x2))
% U422: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),x3),x2),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5))))),equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8)))))
% U830: < d4 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3)),equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9))))),x2))
% U841: < d4 v20 dv10 f19 c0 t39 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x5),x3)),x6),x5),equivalent_2(x6,equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8)))))),x2))
% U1172: < d4 v18 dv9 f17 c0 t35 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,x2)),x3))),x5)),x0)),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))
% U1179: < d4 v22 dv11 f21 c0 t43 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,x2)),x3))),x5)),x0)),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9)))),x6))))
% U1360: < d4 v12 dv6 f17 c6 t35 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),equivalent_2(equivalent_2(equivalent_2(x1,x5),x0),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0())))))))
% U1492: < d4 v18 dv9 f23 c6 t47 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),equivalent_2(equivalent_2(equivalent_2(x1,x5),x0),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0())))))),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))
% U1586: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x1,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0)))
% U1780: < d4 v14 dv7 f19 c6 t39 td11 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x0,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5))))),x2))),equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))))
% U1909: < d4 v20 dv10 f19 c0 t39 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x5),x3)),x6),x5)),equivalent_2(x6,equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8))))))
% U1958: < d4 v18 dv9 f17 c0 t35 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(x3,x4)),equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,equivalent_2(x8,x5)),x6))),x8)),x3)))
% U1964: < d4 v22 dv11 f21 c0 t43 td10 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,x6)),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,equivalent_2(x10,x7)),x8))),x10)),x5)))
% U2099: < d4 v18 dv9 f17 c0 t35 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x4,x1)),x2))),x4)),x5),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))),equivalent_2(x5,x0)))
% U3282: < d4 v14 dv7 f19 c6 t39 td11 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x2,x6)))
% U6521: < d4 v28 dv14 f27 c0 t55 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,x6)),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,equivalent_2(x10,x7)),x8))),x10)),x5)),equivalent_2(x11,equivalent_2(equivalent_2(x12,x13),equivalent_2(equivalent_2(x13,x11),x12)))))
% U6971: < d4 v16 dv8 f21 c6 t43 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x2),x6)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))))
% U9216: < d4 v28 dv14 f27 c0 t55 td11 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3)),equivalent_2(x8,x9))),equivalent_2(equivalent_2(x9,equivalent_2(equivalent_2(x10,equivalent_2(equivalent_2(x11,x12),equivalent_2(equivalent_2(x12,equivalent_2(x13,x10)),x11))),x13)),x8)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), x0))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4)))), x2)) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5)))), x2))), x0))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U9:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2)) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x4), x2)), equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6)))), x4)), x0))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U16:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_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(b_0(), equivalent_2(c_0(), a_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(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_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(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2)) ....... U4
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0())))), x1)), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4)))))) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))), x3)), x5))) ....... R4 [R3:L1, U3:L0]
% Derivation of unit clause U59:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), x0)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2)))), x4), equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6)))), equivalent_2(x4, x0))) ....... R4 [R3:L0, U3:L0]
% Derivation of unit clause U106:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))) ....... R3 [R2:L1, U1:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),x3)),x5))) ....... U16
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), x5), equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))), equivalent_2(x5, x3)))) ....... R4 [R3:L1, U16:L0]
% Derivation of unit clause U159:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x4)),x0))) ....... U9
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | is_a_theorem_1(equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x7), x5)), equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9)))), x7)), x3)) ....... R3 [R2:L1, U9:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2)))), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x7), x5)), equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9)))), x7)), equivalent_2(x4, x0))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U160:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x4)),x0))) ....... U9
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | is_a_theorem_1(equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x7), x5)), equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9)))), x7)), x3)) ....... R3 [R2:L1, U9:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x3), x1)), equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5)))), x3)), equivalent_2(equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x0), x7)), equivalent_2(x9, equivalent_2(equivalent_2(x10, x11), equivalent_2(equivalent_2(x11, x9), x10)))))) ....... R4 [R3:L0, U3:L0]
% Derivation of unit clause U171:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x1),x2)))),x4),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),equivalent_2(x4,x0))) ....... U59
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5)))), x7), equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9)))))) | is_a_theorem_1(equivalent_2(x7, x3)) ....... R3 [R2:L1, U59:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7))))), x3)), x5))) ....... R4 [R3:L0, U3:L0]
% Derivation of unit clause U179:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x1),x2)))),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x7),x5)),equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9)))),x7)),equivalent_2(x4,x0))) ....... U159
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5)))), x7), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x10), x8)), equivalent_2(x11, equivalent_2(equivalent_2(x12, x13), equivalent_2(equivalent_2(x13, x11), x12)))), x10)))) | is_a_theorem_1(equivalent_2(x7, x3)) ....... R3 [R2:L1, U159:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))), x0)), x2)) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U181:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x3),x1)),equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))),x3)),equivalent_2(equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x0),x7)),equivalent_2(x9,equivalent_2(equivalent_2(x10,x11),equivalent_2(equivalent_2(x11,x9),x10)))))) ....... U160
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x6), x4)), equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8)))), x6)))) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x10, x11), equivalent_2(equivalent_2(x11, x3), x10)), equivalent_2(x12, equivalent_2(equivalent_2(x13, x14), equivalent_2(equivalent_2(x14, x12), x13))))) ....... R3 [R2:L1, U160:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), x0)), equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6))))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U225:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, x4)) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),x5),equivalent_2(x4,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x5,x3)))) ....... U106
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | ~is_a_theorem_1(equivalent_2(x3, equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x7, x8), x9), equivalent_2(x8, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))), equivalent_2(x9, x7))))) ....... R3 [R2:L2, U106:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4)))), x2), equivalent_2(equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), x11), equivalent_2(x10, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))), equivalent_2(x11, x9))))) ....... R4 [R3:L0, U3:L0]
% Derivation of unit clause U342:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | ~is_a_theorem_1(x3) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))) | is_a_theorem_1(x2) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),x2)) ....... U179
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))) ....... R4 [R3:L0, U179:L0]
% Derivation of unit clause U361:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | ~is_a_theorem_1(x3) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))))),x3)),x5))) ....... U171
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))), x0))) | is_a_theorem_1(x2) ....... R3 [R2:L0, U171:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))))),x3)),x5))) ....... U171
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), x3), x2), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5)))))) ....... R4 [R3:L0, U171:L0]
% Derivation of unit clause U376:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | ~is_a_theorem_1(x3) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))) ....... U342
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R3 [R2:L0, U342:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),x3),x2),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))))) ....... U361
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x4), x2)), x5), x4), equivalent_2(x5, equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7)))))), x0))) ....... R4 [R3:L0, U361:L0]
% Derivation of unit clause U420:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | ~is_a_theorem_1(x3) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),x5),x4),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))),x0))) ....... U376
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x5), x3)), x6), x5), equivalent_2(x6, equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8))))))) | is_a_theorem_1(x2) ....... R3 [R2:L0, U376:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))),x2))),x0))) ....... U8
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6)))), x3))), x2)) ....... R4 [R3:L0, U8:L0]
% Derivation of unit clause U422:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4))) | ~is_a_theorem_1(x3) | is_a_theorem_1(x4) ....... R2 [R1:L1, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),x5),x4),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))),x0))) ....... U376
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x5), x3)), x6), x5), equivalent_2(x6, equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8))))))) | is_a_theorem_1(x2) ....... R3 [R2:L0, U376:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),x2)) ....... U179
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), x3), x2), equivalent_2(x3, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5))))), equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8))))) ....... R4 [R3:L0, U179:L0]
% Derivation of unit clause U830:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3))), x0))) ....... R2 [R1:L0, B2:L2]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), x3), x2)) | ~is_a_theorem_1(x3) ....... R3 [R2:L2, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6))))) ....... U181
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6)))), x3)), equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9))))), x2)) ....... R4 [R3:L1, U181:L0]
% Derivation of unit clause U841:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3))), x0))) ....... R2 [R1:L0, B2:L2]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), x3), x2)) | ~is_a_theorem_1(x3) ....... R3 [R2:L2, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),x3),x2),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5)))))) ....... U361
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, x2), x0)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x5), x3)), x6), x5), equivalent_2(x6, equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8)))))), x2)) ....... R4 [R3:L1, U361:L0]
% Derivation of unit clause U1172:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3))), x0))) ....... R2 [R1:L0, B2:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),x5),x4),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))),x0))) ....... U376
% is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, equivalent_2(x4, x1)), x2))), x4))) ....... R3 [R2:L2, U376:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2)) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, x2)), x3))), x5)), x0)), equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7))))) ....... R4 [R3:L1, U4:L0]
% Derivation of unit clause U1179:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3))), x0))) ....... R2 [R1:L0, B2:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,x4),x2)),x5),x4),equivalent_2(x5,equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))))),x0))) ....... U376
% is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, equivalent_2(x4, x1)), x2))), x4))) ....... R3 [R2:L2, U376:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3))),x2)) ....... U420
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, x2)), x3))), x5)), x0)), equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, equivalent_2(x8, equivalent_2(equivalent_2(x9, x10), equivalent_2(equivalent_2(x10, x8), x9)))), x6)))) ....... R4 [R3:L1, U420:L0]
% Derivation of unit clause U1360:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0))) ....... U3
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x0), x2), equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4)))), equivalent_2(x2, x1))) ....... R3 [R2:L1, U3:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4)))),x2),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),x11),equivalent_2(x10,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x11,x9))))) ....... U225
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), equivalent_2(equivalent_2(equivalent_2(x1, x5), x0), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))))) ....... R4 [R3:L1, U225:L0]
% Derivation of unit clause U1492:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),x2)) ....... U179
% ~is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2))))) | is_a_theorem_1(x0) ....... R3 [R2:L1, U179:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),equivalent_2(equivalent_2(equivalent_2(x1,x5),x0),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))))) ....... U1360
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), equivalent_2(equivalent_2(equivalent_2(x1, x5), x0), equivalent_2(x5, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0())))))), equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7))))) ....... R4 [R3:L1, U1360:L0]
% Derivation of unit clause U1586:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3)),equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9))))),x2)) ....... U830
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2)))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x0), x4)), x6))) | is_a_theorem_1(x6) ....... R3 [R2:L1, U830:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x1, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))), equivalent_2(x2, x0))) ....... R4 [R3:L0, U1:L0]
% Derivation of unit clause U1780:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x5),x3)),x6),x5),equivalent_2(x6,equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8)))))),x2)) ....... U841
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x3), x1)), x0), x3)) ....... R3 [R2:L1, U841:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),equivalent_2(equivalent_2(equivalent_2(x1,x5),x0),equivalent_2(x5,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0())))))),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))))) ....... U1492
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, equivalent_2(x0, equivalent_2(x4, equivalent_2(equivalent_2(x5, x6), equivalent_2(equivalent_2(x6, x4), x5))))), x2))), equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0())))))) ....... R4 [R3:L1, U1492:L0]
% Derivation of unit clause U1909:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... 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(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0))) ....... U1586
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), x1)) ....... R3 [R2:L1, U1586:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x2),x0)),x3),x2),equivalent_2(x3,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5))))),equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8))))) ....... U422
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x5), x3)), x6), x5)), equivalent_2(x6, equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, x7), x8)))))) ....... R4 [R3:L0, U422:L0]
% Derivation of unit clause U1958:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... 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(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0))) ....... U1586
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), x1)) ....... R3 [R2:L1, U1586:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,x2)),x3))),x5)),x0)),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7))))) ....... U1172
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(x3, x4)), equivalent_2(equivalent_2(x4, equivalent_2(equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, equivalent_2(x8, x5)), x6))), x8)), x3))) ....... R4 [R3:L0, U1172:L0]
% Derivation of unit clause U1964:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... 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(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0))) ....... U1586
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), x1)) ....... R3 [R2:L1, U1586:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,x2)),x3))),x5)),x0)),equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,equivalent_2(x8,equivalent_2(equivalent_2(x9,x10),equivalent_2(equivalent_2(x10,x8),x9)))),x6)))) ....... U1179
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), x0)), equivalent_2(x5, x6)), equivalent_2(equivalent_2(x6, equivalent_2(equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, equivalent_2(x10, x7)), x8))), x10)), x5))) ....... R4 [R3:L0, U1179:L0]
% Derivation of unit clause U2099:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... 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(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0))) ....... U1586
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), x1)) ....... R3 [R2:L1, U1586:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(x3,x4)),equivalent_2(equivalent_2(x4,equivalent_2(equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,equivalent_2(x8,x5)),x6))),x8)),x3))) ....... U1958
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, equivalent_2(x4, x1)), x2))), x4)), x5), equivalent_2(x6, equivalent_2(equivalent_2(x7, x8), equivalent_2(equivalent_2(x8, x6), x7)))), equivalent_2(x5, x0))) ....... R4 [R3:L0, U1958:L0]
% Derivation of unit clause U3282:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... 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(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),equivalent_2(x2,x0))) ....... U1586
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), x2)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), x1)) ....... R3 [R2:L1, U1586:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x0,equivalent_2(x4,equivalent_2(equivalent_2(x5,x6),equivalent_2(equivalent_2(x6,x4),x5))))),x2))),equivalent_2(x1,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0())))))) ....... U1780
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))), x0)), equivalent_2(x6, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0()))))), equivalent_2(x2, x6))) ....... R4 [R3:L1, U1780:L0]
% Derivation of unit clause U6521:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x5),x3)),x6),x5)),equivalent_2(x6,equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8)))))) ....... U1909
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2))))) ....... R3 [R2:L1, U1909:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,x6)),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,equivalent_2(x10,x7)),x8))),x10)),x5))) ....... U1964
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, x2), x3)))), x0)), equivalent_2(x5, x6)), equivalent_2(equivalent_2(x6, equivalent_2(equivalent_2(x7, equivalent_2(equivalent_2(x8, x9), equivalent_2(equivalent_2(x9, equivalent_2(x10, x7)), x8))), x10)), x5)), equivalent_2(x11, equivalent_2(equivalent_2(x12, x13), equivalent_2(equivalent_2(x13, x11), x12))))) ....... R4 [R3:L0, U1964:L0]
% Derivation of unit clause U6971:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x5),x3)),x6),x5)),equivalent_2(x6,equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,x7),x8)))))) ....... U1909
% ~is_a_theorem_1(x0) | is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x3, x1), x2))))) ....... R3 [R2:L1, U1909:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),equivalent_2(x6,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0()))))),equivalent_2(x2,x6))) ....... U3282
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x5, x3), x4))))), x0)), equivalent_2(equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x2), x6)), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(b_0(), equivalent_2(c_0(), a_0())))))) ....... R4 [R3:L1, U3282:L0]
% Derivation of unit clause U9216:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1)))) ....... 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(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))) ....... R1 [B1:L0, B2:L1]
% ~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(equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1)), x3)) | is_a_theorem_1(x3) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(equivalent_2(x3,equivalent_2(x4,x1)),x2))),x4)),x5),equivalent_2(x6,equivalent_2(equivalent_2(x7,x8),equivalent_2(equivalent_2(x8,x6),x7)))),equivalent_2(x5,x0))) ....... U2099
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(x3, x0), equivalent_2(x1, x2))) ....... R3 [R2:L1, U2099:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,x2),x3)))),x0)),equivalent_2(x5,x6)),equivalent_2(equivalent_2(x6,equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(x8,x9),equivalent_2(equivalent_2(x9,equivalent_2(x10,x7)),x8))),x10)),x5)),equivalent_2(x11,equivalent_2(equivalent_2(x12,x13),equivalent_2(equivalent_2(x13,x11),x12))))) ....... U6521
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x0), x1))), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(equivalent_2(x7, x5), x6)))), x3)), equivalent_2(x8, x9))), equivalent_2(equivalent_2(x9, equivalent_2(equivalent_2(x10, equivalent_2(equivalent_2(x11, x12), equivalent_2(equivalent_2(x12, equivalent_2(x13, x10)), x11))), x13)), x8))) ....... R4 [R3:L0, U6521:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x0),x1))),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x5),x6)))),x3)),equivalent_2(x8,x9))),equivalent_2(equivalent_2(x9,equivalent_2(equivalent_2(x10,equivalent_2(equivalent_2(x11,x12),equivalent_2(equivalent_2(x12,equivalent_2(x13,x10)),x11))),x13)),x8))) ....... U9216
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x5,x3),x4))))),x0)),equivalent_2(equivalent_2(equivalent_2(x6,x7),equivalent_2(equivalent_2(x7,x2),x6)),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(b_0(),equivalent_2(c_0(),a_0())))))) ....... U6971
% [] ....... R1 [U9216:L0, U6971:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 447087
% resolvents: 447078 factors: 9
% Number of unit clauses generated: 445082
% % unit clauses generated to total clauses generated: 99.55
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 10 [4] = 9205
% Total = 9217
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 445082 [2] = 1991 [3] = 14
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)1587 (-)7630
% ------------------
% Total: (+)1587 (-)7630
% Total number of unit clauses retained: 9217
% Number of clauses skipped because of their length: 1950
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 447215
% Number of unification failures: 548553
% Number of unit to unit unification failures: 12107074
% N literal unification failure due to lookup root_id table: 29
% 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: 26
% N unit clauses dropped because they exceeded max values: 435528
% N unit clauses dropped because too much nesting: 277384
% N unit clauses not constrcuted because table was full: 0
% N unit clauses dropped because UCFA table was full: 0
% Max number of terms in a unit clause: 63
% Max term depth in a unit clause: 11
% Number of states in UCFA table: 204432
% Total number of terms of all unit clauses in table: 494887
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.39
% Ratio n states used/total unit clauses terms: 0.41
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 995768
% ConstructUnitClause() = 444743
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 1.46 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 13150
% | |
% --------------------------------------------------------
% Elapsed time: 34 secs
% CPU time: 34.45 secs
%
%------------------------------------------------------------------------------