TSTP Solution File: LCL011-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL011-1 : 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 23:16:42 EST 2010
% Result : Unsatisfiable 0.41s
% Output : Refutation 0.41s
% 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/SystemOnTPTP25879/LCL/LCL011-1+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 = 80] [nf = 0] [nu = 32] [ut = 29]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 197] [nf = 5] [nu = 96] [ut = 29]
% 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(a_0(),b_0()),equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0()))))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2))))
% 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 td4 b > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2))))
% U3: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0)))
% U4: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,x1),x0)),equivalent_2(x2,x3)))
% U8: < d2 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(equivalent_2(x4,x2),equivalent_2(x3,x4)),x1),x0)))
% U10: < d2 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x3),equivalent_2(x4,x5)),x2),x1),x0)))
% U43: < d4 v4 dv2 f9 c6 t19 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x0),equivalent_2(equivalent_2(a_0(),b_0()),x1)),equivalent_2(x1,x0)))
% U443: < d4 v12 dv6 f17 c6 t35 td7 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x4),equivalent_2(equivalent_2(a_0(),b_0()),x5)),equivalent_2(x5,x4))))
% U692: < 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(x2,x0)),x3),x4),equivalent_2(equivalent_2(x5,equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x6),x5))))
% U702: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x2,x5)),equivalent_2(x5,x4)),x1),x0)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... U1
% Derivation of unit clause U3:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(x2,x0),equivalent_2(x1,x2)))) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), x0))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), x3)) | is_a_theorem_1(x3) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U8:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x2), equivalent_2(x3, x4)), x1), x0))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U10:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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(x0, x1)) | is_a_theorem_1(equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x2),equivalent_2(x3,x4)),x1),x0))) ....... U8
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, equivalent_2(x3, x4)))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x3), equivalent_2(x4, x5)), x2), x1), x0))) ....... R2 [R1:L0, U8:L0]
% Derivation of unit clause U43:
% ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),b_0()),equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_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(a_0(), b_0()), equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_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(a_0(), b_0()), equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_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(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,x1),x0)),equivalent_2(x2,x3))) ....... U4
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(x2, equivalent_2(a_0(), b_0()))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x2), x1)))) ....... R3 [R2:L0, U4:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x0), equivalent_2(equivalent_2(a_0(), b_0()), x1)), equivalent_2(x1, x0))) ....... R4 [R3:L1, U3:L0]
% Derivation of unit clause U443:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(x2,x0),equivalent_2(x1,x2)))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U1:L0]
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x0),equivalent_2(equivalent_2(a_0(),b_0()),x1)),equivalent_2(x1,x0))) ....... U43
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x1), equivalent_2(x2, x3)), x0)), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(), c_0()), equivalent_2(c_0(), b_0())), x4), equivalent_2(equivalent_2(a_0(), b_0()), x5)), equivalent_2(x5, x4)))) ....... R4 [R3:L1, U43:L0]
% Derivation of unit clause U692:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,equivalent_2(x3,x4)))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5,x3),equivalent_2(x4,x5)),x2),x1),x0))) ....... U10
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x2, x0)), x3), x4), equivalent_2(equivalent_2(x5, equivalent_2(x6, x4)), equivalent_2(equivalent_2(equivalent_2(x3, equivalent_2(x1, x2)), x6), x5)))) ....... R4 [R3:L0, U10:L0]
% Derivation of unit clause U702:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x1,x2)))) ....... 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), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x1, x2))), 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(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0))) ....... U3
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x1), x0)), equivalent_2(x2, x3)), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x2,x0)),x3),x4),equivalent_2(equivalent_2(x5,equivalent_2(x6,x4)),equivalent_2(equivalent_2(equivalent_2(x3,equivalent_2(x1,x2)),x6),x5)))) ....... U692
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, equivalent_2(x2, x3))), equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x2, x5)), equivalent_2(x5, x4)), x1), x0))) ....... R4 [R3:L0, U692:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,equivalent_2(x2,x3))),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x2,x5)),equivalent_2(x5,x4)),x1),x0))) ....... U702
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x1),equivalent_2(x2,x3)),x0)),equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(a_0(),c_0()),equivalent_2(c_0(),b_0())),x4),equivalent_2(equivalent_2(a_0(),b_0()),x5)),equivalent_2(x5,x4)))) ....... U443
% [] ....... R1 [U702:L0, U443:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 2179
% resolvents: 2170 factors: 9
% Number of unit clauses generated: 1995
% % unit clauses generated to total clauses generated: 91.56
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 27 [4] = 674
% Total = 703
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 1995 [2] = 173 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)40 (-)663
% ------------------
% Total: (+)40 (-)663
% Total number of unit clauses retained: 703
% Number of clauses skipped because of their length: 83
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 2203
% Number of unification failures: 1546
% Number of unit to unit unification failures: 26274
% 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: 15
% N unit clauses dropped because they exceeded max values: 833
% N unit clauses dropped because too much nesting: 299
% 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: 15424
% Total number of terms of all unit clauses in table: 32965
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.03
% Ratio n states used/total unit clauses terms: 0.47
% Number of symbols (columns) in UCFA: 39
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 3749
% ConstructUnitClause() = 1534
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.40 secs
%
%------------------------------------------------------------------------------