%------------------------------------------------------------------------------
% File     : CARINE---0.734
% Problem  : LCL096-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm  : add_equality
% Format   : carine
% Command  : carine %s t=%d xo=off uct=32000

% Computer : art03.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 : Sat Nov 27 23:59:11 EST 2010

% Result   : Unsatisfiable 0.72s
% Output   : Refutation 0.72s
% 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/SystemOnTPTP24255/LCL/LCL096-1+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 = 7] [nf = 0] [nu = 0] [ut = 4]
% Looking for a proof at depth = 2 ...
% +================================================+
% |                                                |
% | 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(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0()))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3))))
% B2: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4))
% B3: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3))
% B4: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v10 dv5 f9 c0 t19 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3))))
% U2: < d0 v10 dv5 f9 c0 t19 td7 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4))
% U5: < d2 v10 dv5 f15 c6 t31 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0())))
% U9: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(equivalent_2(x0,x5),x4),equivalent_2(equivalent_2(x1,x5),x3)))))
% U125: < d2 v8 dv4 f13 c6 t27 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0()))
% U312: < d2 v18 dv9 f23 c6 t47 td9 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7)),x8),equivalent_2(equivalent_2(x6,x7),x8)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())))
% U322: < d2 v12 dv6 f11 c0 t23 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x0),equivalent_2(equivalent_2(equivalent_2(x2,x5),x4),equivalent_2(equivalent_2(x3,x5),x1)))))
% U1686: < d2 v26 dv13 f31 c6 t63 td10 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8),x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x9,x11)),x12),equivalent_2(equivalent_2(x10,x11),x12)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0()))))
% U1900: < d2 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x2),equivalent_2(equivalent_2(x1,x7),x6))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... U1
% Derivation of unit clause U2:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U2
% Derivation of unit clause U5:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),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) ....... B4
%  ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0())), c_0()), c_0()))) ....... R1 [B0:L0, B4:L2]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... U2
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), equivalent_2(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0())), c_0()), c_0()))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U9:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(equivalent_2(x0, x4), x2), equivalent_2(equivalent_2(x1, x4), x3))), x5)) | is_a_theorem_1(x5) ....... R1 [B1:L0, B4:L0]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... U1
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(equivalent_2(x0, x5), x4), equivalent_2(equivalent_2(x1, x5), x3))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U125:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(equivalent_2(x0,x4),x2),equivalent_2(equivalent_2(x1,x4),x3)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x3)) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x4), x2), equivalent_2(equivalent_2(x1, x4), x3))) ....... R1 [B1:L0, B4:L1]
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0())),c_0()),c_0()))) ....... U5
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0())) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U312:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), x5)) | is_a_theorem_1(x5) ....... R1 [B2:L0, B4:L0]
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())) ....... U125
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4), x4), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7)), x8), equivalent_2(equivalent_2(x6, x7), x8)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0()))) ....... R2 [R1:L1, U125:L0]
% Derivation of unit clause U322:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B2:L0, B4:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(equivalent_2(x0,x5),x4),equivalent_2(equivalent_2(x1,x5),x3))))) ....... U9
%   is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), x4), x0), equivalent_2(equivalent_2(equivalent_2(x2, x5), x4), equivalent_2(equivalent_2(x3, x5), x1))))) ....... R2 [R1:L0, U9:L0]
% Derivation of unit clause U1686:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4)) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B2:L0, B4:L1]
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),x4),x4),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x6),equivalent_2(x5,x7)),x8),equivalent_2(equivalent_2(x6,x7),x8)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0()))) ....... U312
%   ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7), equivalent_2(equivalent_2(x5, x6), x7)), x8), x8), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9, x10), equivalent_2(x9, x11)), x12), equivalent_2(equivalent_2(x10, x11), x12)), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), b_0()), a_0()))), c_0()), c_0())))) ....... R2 [R1:L1, U312:L0]
% Derivation of unit clause U1900:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),x3),x3)) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B4
%  ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3), x3), x4)) | is_a_theorem_1(x4) ....... R1 [B3:L0, B4:L0]
%  is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),x4),x0),equivalent_2(equivalent_2(equivalent_2(x2,x5),x4),equivalent_2(equivalent_2(x3,x5),x1))))) ....... U322
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x6)), equivalent_2(equivalent_2(equivalent_2(x0, x7), x2), equivalent_2(equivalent_2(x1, x7), x6)))) ....... R2 [R1:L0, U322:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),x6)),equivalent_2(equivalent_2(equivalent_2(x0,x7),x2),equivalent_2(equivalent_2(x1,x7),x6)))) ....... U1900
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),x3),equivalent_2(equivalent_2(x1,x2),x3)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7),equivalent_2(equivalent_2(x5,x6),x7)),x8),x8),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x9,x10),equivalent_2(x9,x11)),x12),equivalent_2(equivalent_2(x10,x11),x12)),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),b_0()),a_0()))),c_0()),c_0())))) ....... U1686
%  [] ....... R1 [U1900:L0, U1686:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% |                Statistics                 |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 2334
% 	resolvents: 2334	factors: 0
% Number of unit clauses generated: 2321
% % unit clauses generated to total clauses generated: 99.44
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 4		[2] = 1897	
% Total = 1901
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 2321	[2] = 13	
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1	(+)1829	(-)72
% 			------------------
% 		Total:	(+)1829	(-)72
% Total number of unit clauses retained: 1901
% Number of clauses skipped because of their length: 5
% N base clauses skippped in resolve-with-all-base-clauses
% 	because of the shortest resolvents table: 0
% Number of successful unifications: 2348
% Number of unification failures: 161
% Number of unit to unit unification failures: 131676
% N literal unification failure due to lookup root_id table: 9
% 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: 16
% N unit clauses dropped because they exceeded max values: 424
% N unit clauses dropped because too much nesting: 39
% 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: 34644
% Total number of terms of all unit clauses in table: 86411
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.07
% Ratio n states used/total unit clauses terms: 0.40
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 2509
% ConstructUnitClause() = 2321
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.05 secs
% --------------------------------------------------------
% |                                                      |
%   Inferences per sec: inf
% |                                                      |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 0.72 secs
% 
%------------------------------------------------------------------------------