%------------------------------------------------------------------------------
% File     : CARINE---0.734
% Problem  : LCL098-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm  : add_equality
% Format   : carine
% Command  : carine %s t=%d xo=off uct=32000

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Nov 27 23:59:33 EST 2010

% Result   : Unsatisfiable 0.36s
% Output   : Refutation 0.36s
% 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/SystemOnTPTP22922/LCL/LCL098-1+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 ...
% +================================================+
% |                                                |
% | Congratulations!!! ........ A proof was found. |
% |                                                |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0()))))
% B1: 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)
% Unit Clauses:
% --------------
% U1: < 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))
% U3: < d2 v8 dv4 f17 c10 t35 td6 > ~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(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0())))))
% U4: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2))))
% U5: < d2 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x5),equivalent_2(equivalent_2(x3,x4),x5)),x0),x1)))
% U6: < d2 v18 dv9 f17 c0 t35 td8 > 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)),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))
% U7: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x0),equivalent_2(equivalent_2(x3,x4),x1))))
% U13: < d2 v14 dv7 f13 c0 t27 td6 > 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,x4),equivalent_2(x3,x5)),x6)),equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x4,x5),x6))))
% U16: < d2 v10 dv5 f9 c0 t19 td6 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(x0,equivalent_2(x1,x4)),x3))))
% U18: < 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),equivalent_2(x2,x4)),equivalent_2(x5,x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x1)))))
% U20: < d2 v16 dv8 f15 c0 t31 td7 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7))),equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,equivalent_2(equivalent_2(x5,x6),x7)))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% 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)) ....... U1
% Derivation of unit clause U3:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_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(equivalent_2(a_0(), b_0()), c_0()), e_0()), equivalent_2(equivalent_2(equivalent_2(a_0(), falsehood_0()), c_0()), equivalent_2(equivalent_2(b_0(), falsehood_0()), e_0()))))) ....... R1 [B0:L0, B2: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)) ....... U1
%   ~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(a_0(), b_0()), c_0()), e_0()), equivalent_2(equivalent_2(equivalent_2(a_0(), falsehood_0()), c_0()), equivalent_2(equivalent_2(b_0(), falsehood_0()), e_0()))))) ....... R2 [R1:L1, U1:L0]
% Derivation of unit clause U4:
% 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)) ....... 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(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 [B1:L0, B2:L0]
%  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)) ....... U1
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(equivalent_2(x3, x1), equivalent_2(equivalent_2(x0, x3), x2)))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U5:
% 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)) ....... 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(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 [B1:L0, B2:L0]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(equivalent_2(x3,x1),equivalent_2(equivalent_2(x0,x3),x2)))) ....... U4
%   is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), x5), equivalent_2(equivalent_2(x3, x4), x5)), x0), x1))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U6:
% 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)) ....... 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(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 [B1:L0, B2:L0]
%  is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x5),equivalent_2(equivalent_2(x3,x4),x5)),x0),x1))) ....... U5
%   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)), 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)) ....... R2 [R1:L0, U5:L0]
% Derivation of unit clause U7:
% 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)) ....... 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(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 [B1:L0, B2:L0]
%  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)),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)) ....... U6
%   is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), x0), equivalent_2(equivalent_2(x3, x4), x1)))) ....... R2 [R1:L0, U6:L0]
% Derivation of unit clause U13:
% 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)) ....... 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), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),x0),equivalent_2(equivalent_2(x3,x4),x1)))) ....... U7
%   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, x4), equivalent_2(x3, x5)), x6)), equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x4, x5), x6)))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U16:
% 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)) ....... 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), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... 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,x4),equivalent_2(x3,x5)),x6)),equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x4,x5),x6)))) ....... U13
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), x3), equivalent_2(equivalent_2(x4, x2), equivalent_2(equivalent_2(x0, equivalent_2(x1, x4)), x3)))) ....... R2 [R1:L0, U13:L0]
% Derivation of unit clause U18:
% 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)) ....... 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), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),x3),equivalent_2(equivalent_2(x4,x2),equivalent_2(equivalent_2(x0,equivalent_2(x1,x4)),x3)))) ....... U16
%   is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x5, x0)), equivalent_2(equivalent_2(x3, x4), equivalent_2(x5, x1))))) ....... R2 [R1:L0, U16:L0]
% Derivation of unit clause U20:
% 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)) ....... 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), equivalent_2(x0, x2)), x3), equivalent_2(equivalent_2(x1, x2), x3)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L1]
%  is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x5,x0)),equivalent_2(equivalent_2(x3,x4),equivalent_2(x5,x1))))) ....... U18
%   is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), x7))), equivalent_2(equivalent_2(x1, x2), equivalent_2(x3, equivalent_2(equivalent_2(x5, x6), x7))))) ....... R2 [R1:L0, U18: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(x3,equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),x7))),equivalent_2(equivalent_2(x1,x2),equivalent_2(x3,equivalent_2(equivalent_2(x5,x6),x7))))) ....... U20
% ~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(a_0(),b_0()),c_0()),e_0()),equivalent_2(equivalent_2(equivalent_2(a_0(),falsehood_0()),c_0()),equivalent_2(equivalent_2(b_0(),falsehood_0()),e_0()))))) ....... U3
%  [] ....... R1 [U20:L0, U3:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% |                Statistics                 |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 34
% 	resolvents: 34	factors: 0
% Number of unit clauses generated: 28
% % unit clauses generated to total clauses generated: 82.35
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2		[2] = 19	
% Total = 21
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 28	[2] = 6	
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1	(+)16	(-)5
% 			------------------
% 		Total:	(+)16	(-)5
% Total number of unit clauses retained: 21
% Number of clauses skipped because of their length: 2
% N base clauses skippped in resolve-with-all-base-clauses
% 	because of the shortest resolvents table: 0
% Number of successful unifications: 52
% Number of unification failures: 2
% Number of unit to unit unification failures: 77
% N literal unification failure due to lookup root_id table: 5
% 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: 11
% N unit clauses dropped because they exceeded max values: 9
% N unit clauses dropped because too much nesting: 0
% 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: 59
% Max term depth in a unit clause: 9
% Number of states in UCFA table: 390
% Total number of terms of all unit clauses in table: 583
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.00
% Ratio n states used/total unit clauses terms: 0.67
% Number of symbols (columns) in UCFA: 41
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 54
% ConstructUnitClause() = 28
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% |                                                      |
%   Inferences per sec: inf
% |                                                      |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.35 secs
% 
%------------------------------------------------------------------------------