TSTP Solution File: LCL006-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL006-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art09.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 23:16:15 EST 2010
% Result : Unsatisfiable 0.95s
% Output : Refutation 0.95s
% 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/SystemOnTPTP25623/LCL/LCL006-1+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 = 1 secs [nr = 5] [nf = 0] [nu = 0] [ut = 3]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 1738] [nf = 0] [nu = 983] [ut = 604]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 4889] [nf = 5] [nu = 3370] [ut = 604]
% 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(c_0(),a_0())),equivalent_2(b_0(),c_0())))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2))))
% B2: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0)))
% B3: ~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 td4 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2))))
% U2: < d0 v4 dv2 f3 c0 t7 td3 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0)))
% U7: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2)))))
% U8: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,x1),x2)))
% U9: < d2 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x0))))
% U10: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x1,x2)))
% U317: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x0))),equivalent_2(x1,x2)))
% U319: < d2 v6 dv3 f5 c0 t11 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)))
% U2270: < d4 v8 dv4 f13 c6 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(equivalent_2(b_0(),c_0()),x3)))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... U1
% Derivation of unit clause U2:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... U2
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, equivalent_2(x0, equivalent_2(x1, x2))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... U2
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x0, x1), x2))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U9:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2))))) ....... U7
% is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(x1, x2), x3), equivalent_2(equivalent_2(x1, equivalent_2(x2, x3)), x0)))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U10:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),equivalent_2(x0,equivalent_2(x1,x2)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), equivalent_2(x0, equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x0,x1),x2))) ....... U8
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), x2), x0), equivalent_2(x1, x2))) ....... R2 [R1:L0, U8:L0]
% Derivation of unit clause U317:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(x1, x0)) ....... R1 [B2:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,equivalent_2(x0,equivalent_2(x1,x2))))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x0))), equivalent_2(x1, x2))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U319:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x1,x0))) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(x0, x1)) | is_a_theorem_1(equivalent_2(x1, x0)) ....... R1 [B2:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),x2),x0),equivalent_2(x1,x2))) ....... U10
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2))) ....... R2 [R1:L0, U10:L0]
% Derivation of unit clause U2270:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(b_0(),c_0()))) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(b_0(), c_0())))) ....... R1 [B0:L0, B3:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(b_0(), c_0())))) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, x0)) ....... R2 [R1:L0, B3:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x0))),equivalent_2(x1,x2))) ....... U317
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(equivalent_2(b_0(), c_0()), x1))))) ....... R3 [R2:L0, U317:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2))) ....... U319
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(equivalent_2(x2, x0), x1), x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), equivalent_2(c_0(), a_0())), equivalent_2(equivalent_2(b_0(), c_0()), x3))))) ....... R4 [R3:L0, U319:L0]
% Derivation of the empty clause:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(equivalent_2(x2,x0),x1),x2)),equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(c_0(),a_0())),equivalent_2(equivalent_2(b_0(),c_0()),x3))))) ....... U2270
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(x1,x2),x3),equivalent_2(equivalent_2(x1,equivalent_2(x2,x3)),x0)))) ....... U9
% [] ....... R1 [U2270:L0, U9:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 7196
% resolvents: 7189 factors: 7
% Number of unit clauses generated: 5659
% % unit clauses generated to total clauses generated: 78.64
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 601 [4] = 1667
% Total = 2271
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 5659 [2] = 1522 [3] = 15
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)165 (-)2106
% ------------------
% Total: (+)165 (-)2106
% Total number of unit clauses retained: 2271
% Number of clauses skipped because of their length: 29
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 7212
% Number of unification failures: 1996
% Number of unit to unit unification failures: 347329
% N literal unification failure due to lookup root_id table: 34
% N base clause resolution failure due to lookup table: 0
% N UC-BCL resolution dropped due to lookup table: 24
% Max entries in substitution set: 14
% N unit clauses dropped because they exceeded max values: 769
% N unit clauses dropped because too much nesting: 256
% 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: 10
% Number of states in UCFA table: 33862
% Total number of terms of all unit clauses in table: 88573
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.06
% Ratio n states used/total unit clauses terms: 0.38
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 9208
% ConstructUnitClause() = 3037
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.01 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 0.95 secs
%
%------------------------------------------------------------------------------