%------------------------------------------------------------------------------
% File     : CARINE---0.734
% Problem  : LCL108-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm  : add_equality
% Format   : carine
% Command  : carine %s t=%d xo=off uct=32000

% Computer : art05.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 00:00:59 EST 2010

% Result   : Unsatisfiable 0.38s
% Output   : Refutation 0.38s
% 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/SystemOnTPTP28629/LCL/LCL108-1+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 = 50] [nf = 0] [nu = 18] [ut = 15]
% Looking for a proof at depth = 3 ...
% 	t = 0 secs [nr = 124] [nf = 4] [nu = 55] [ut = 15]
% 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()),equivalent_2(equivalent_2(b_0(),a_0()),c_0())),c_0()))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v14 dv7 f13 c0 t27 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6))))
% U3: < d2 v14 dv7 f13 c0 t27 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3)))
% U4: < d2 v16 dv8 f15 c0 t31 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7)))
% U5: < d2 v18 dv9 f17 c0 t35 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7)))
% U6: < d2 v20 dv10 f19 c0 t39 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x2)),equivalent_2(x3,equivalent_2(x4,x1))),x5)),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(x7,x8)),equivalent_2(x6,equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8)))),x5)))
% U7: < d2 v22 dv11 f21 c0 t43 td9 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(x6,x8)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(x7,x8)))),x9)),equivalent_2(equivalent_2(equivalent_2(x10,x2),equivalent_2(x10,x3)),x9)))
% U8: < d2 v24 dv12 f23 c0 t47 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),equivalent_2(x5,equivalent_2(x6,x8))),x9)),equivalent_2(equivalent_2(equivalent_2(x10,equivalent_2(x11,x7)),equivalent_2(x10,equivalent_2(x11,x8))),x9)))
% U36: < d4 v10 dv5 f15 c6 t31 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x3))),equivalent_2(x1,x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(b_0(),a_0()),c_0())),c_0())))
% U99: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5))
% U102: < d4 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)))
% U105: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5))
% U107: < d4 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3))))
% U198: < d4 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,equivalent_2(x4,x1)),equivalent_2(x3,equivalent_2(x4,x5)))),equivalent_2(x2,x5)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... U1
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x1), equivalent_2(x2, x0)), x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(equivalent_2(x6, x4), equivalent_2(x6, x5))), x3))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x1),equivalent_2(x2,x0)),x3)),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(equivalent_2(x6,x4),equivalent_2(x6,x5))),x3))) ....... U3
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6))), equivalent_2(x3, equivalent_2(x5, x6))), x7)), equivalent_2(equivalent_2(x1, x2), x7))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U5:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(equivalent_2(x8, x5), equivalent_2(x8, x6)), x7))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U5
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x4, x2)), equivalent_2(x3, equivalent_2(x4, x1))), x5)), equivalent_2(equivalent_2(equivalent_2(x6, equivalent_2(x7, x8)), equivalent_2(x6, equivalent_2(equivalent_2(x9, x7), equivalent_2(x9, x8)))), x5))) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x4,x2)),equivalent_2(x3,equivalent_2(x4,x1))),x5)),equivalent_2(equivalent_2(equivalent_2(x6,equivalent_2(x7,x8)),equivalent_2(x6,equivalent_2(equivalent_2(x9,x7),equivalent_2(x9,x8)))),x5))) ....... U6
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(x1, x3))), equivalent_2(equivalent_2(equivalent_2(x4, equivalent_2(x5, equivalent_2(equivalent_2(x6, x7), equivalent_2(x6, x8)))), equivalent_2(x4, equivalent_2(x5, equivalent_2(x7, x8)))), x9)), equivalent_2(equivalent_2(equivalent_2(x10, x2), equivalent_2(x10, x3)), x9))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6)))) | is_a_theorem_1(equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(x1,x3))),equivalent_2(equivalent_2(equivalent_2(x4,equivalent_2(x5,equivalent_2(equivalent_2(x6,x7),equivalent_2(x6,x8)))),equivalent_2(x4,equivalent_2(x5,equivalent_2(x7,x8)))),x9)),equivalent_2(equivalent_2(equivalent_2(x10,x2),equivalent_2(x10,x3)),x9))) ....... U7
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x3, x4)))), equivalent_2(equivalent_2(equivalent_2(x5, equivalent_2(x6, x7)), equivalent_2(x5, equivalent_2(x6, x8))), x9)), equivalent_2(equivalent_2(equivalent_2(x10, equivalent_2(x11, x7)), equivalent_2(x10, equivalent_2(x11, x8))), x9))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U36:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(b_0(),a_0()),c_0())),c_0())) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(equivalent_2(b_0(), a_0()), c_0())), c_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()), equivalent_2(equivalent_2(b_0(), a_0()), c_0())), c_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,equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3))),equivalent_2(x0,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7)),equivalent_2(equivalent_2(equivalent_2(x8,x5),equivalent_2(x8,x6)),x7))) ....... U5
%    ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(equivalent_2(b_0(), a_0()), c_0())), c_0()))) | ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4))), equivalent_2(x1, equivalent_2(x3, x4))), equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7)), x8)), equivalent_2(equivalent_2(equivalent_2(x9, x6), equivalent_2(x9, x7)), x8)), x0)) ....... R3 [R2:L1, U5:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%     ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x3))), equivalent_2(x1, x3)), x4), x4), equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(equivalent_2(b_0(), a_0()), c_0())), c_0()))) ....... R4 [R3:L1, U4:L0]
% Derivation of unit clause U99:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%    ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U4:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%     is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x1, equivalent_2(x3, x4))), x5), x5)) ....... R4 [R3:L0, U4:L0]
% Derivation of unit clause U102:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%    ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U4:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x1,equivalent_2(x3,x4))),x5),x5)) ....... U99
%     is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2))) ....... R4 [R3:L0, U99:L0]
% Derivation of unit clause U105:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%    ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U4:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U102
%     is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)))), equivalent_2(x0, equivalent_2(x1, equivalent_2(x3, x4)))), x5), x5)) ....... R4 [R3:L0, U102:L0]
% Derivation of unit clause U107:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6))),equivalent_2(x3,equivalent_2(x5,x6))),x7)),equivalent_2(equivalent_2(x1,x2),x7))) ....... U4
%    ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3))), equivalent_2(x0, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7)), equivalent_2(equivalent_2(x5, x6), x7)), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U4:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),x5),x5)) ....... U105
%     is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(x2, x4)), x0), equivalent_2(x4, x3)))) ....... R4 [R3:L0, U105:L0]
% Derivation of unit clause U198:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(equivalent_2(x5,x4),equivalent_2(x5,x3)),x6))),equivalent_2(x2,equivalent_2(equivalent_2(x1,x0),x6)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | is_a_theorem_1(x7) ....... R1 [B1:L0, B2:L0]
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(equivalent_2(x5, x4), equivalent_2(x5, x3)), x6))), equivalent_2(x2, equivalent_2(equivalent_2(x1, x0), x6))), x7)) | ~is_a_theorem_1(equivalent_2(x7, x8)) | is_a_theorem_1(x8) ....... R2 [R1:L1, B2:L0]
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)))),equivalent_2(x0,equivalent_2(x1,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(x5,equivalent_2(x6,x7)),equivalent_2(x5,equivalent_2(x6,x8))),x9)),equivalent_2(equivalent_2(equivalent_2(x10,equivalent_2(x11,x7)),equivalent_2(x10,equivalent_2(x11,x8))),x9))) ....... U8
%    ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(x1, x3))), equivalent_2(equivalent_2(x4, x2), equivalent_2(x4, x3))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U8:L0]
%    is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(x1,equivalent_2(x2,x4)),x0),equivalent_2(x4,x3)))) ....... U107
%     is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(equivalent_2(x3, equivalent_2(x4, x1)), equivalent_2(x3, equivalent_2(x4, x5)))), equivalent_2(x2, x5))) ....... R4 [R3:L0, U107:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(equivalent_2(x3,equivalent_2(x4,x1)),equivalent_2(x3,equivalent_2(x4,x5)))),equivalent_2(x2,x5))) ....... U198
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x3))),equivalent_2(x1,x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(b_0(),a_0()),c_0())),c_0()))) ....... U36
%  [] ....... R1 [U198:L0, U36:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% |                Statistics                 |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 1276
% 	resolvents: 1268	factors: 8
% Number of unit clauses generated: 1133
% % unit clauses generated to total clauses generated: 88.79
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2		[2] = 13	[4] = 184	
% Total = 199
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 1133	[2] = 132	[3] = 11	
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1	(+)55	(-)144
% 			------------------
% 		Total:	(+)55	(-)144
% Total number of unit clauses retained: 199
% Number of clauses skipped because of their length: 75
% N base clauses skippped in resolve-with-all-base-clauses
% 	because of the shortest resolvents table: 0
% Number of successful unifications: 1312
% Number of unification failures: 1064
% Number of unit to unit unification failures: 7801
% N literal unification failure due to lookup root_id table: 26
% N base clause resolution failure due to lookup table: 0
% N UC-BCL resolution dropped due to lookup table: 0
% Max entries in substitution set: 27
% N unit clauses dropped because they exceeded max values: 806
% N unit clauses dropped because too much nesting: 9
% N unit clauses not constrcuted because table was full: 0
% N unit clauses dropped because UCFA table was full: 0
% Max number of terms in a unit clause: 63
% Max term depth in a unit clause: 13
% Number of states in UCFA table: 4977
% Total number of terms of all unit clauses in table: 9201
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.01
% Ratio n states used/total unit clauses terms: 0.54
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 2376
% ConstructUnitClause() = 1003
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.01 secs
% --------------------------------------------------------
% |                                                      |
%   Inferences per sec: inf
% |                                                      |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.37 secs
% 
%------------------------------------------------------------------------------