TSTP Solution File: LCL101-1 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL101-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art02.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 00:00:05 EST 2010
% Result : Unsatisfiable 1.20s
% Output : Refutation 1.20s
% 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/SystemOnTPTP1434/LCL/LCL101-1+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 = 5] [nf = 0] [nu = 0] [ut = 3]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 167] [nf = 0] [nu = 95] [ut = 47]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 408] [nf = 7] [nu = 255] [ut = 47]
% 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()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))
% B1: is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0)))
% B2: 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)
% Unit Clauses:
% --------------
% U1: < d0 v8 dv4 f7 c0 t15 td6 b > is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0)))
% U2: < d0 v8 dv4 f7 c0 t15 td6 b > 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))
% U7: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5))))
% U33: < d2 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)))
% U103: < d4 v2 dv1 f9 c8 t19 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x0,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))
% U104: < d4 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(x3,x4)),equivalent_2(equivalent_2(x5,x0),equivalent_2(x5,x1)))))
% U170: < d4 v12 dv6 f11 c0 t23 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),equivalent_2(x2,x1)))))
% U574: < d4 v16 dv8 f23 c8 t47 td8 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),equivalent_2(x5,x6)),x3)),equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x7,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... U1
% Derivation of unit clause U2:
% 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)) ....... U2
% Derivation of unit clause U7:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% 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)) ....... U2
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U33:
% 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)) ....... 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(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U103:
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_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()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_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(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R2 [R1:L1, B3:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2)),equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)))) ....... U7
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6))), equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0())))))) ....... R3 [R2:L1, U7:L0]
% 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)) ....... U2
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x0, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R4 [R3:L1, U2:L0]
% Derivation of unit clause U104:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% ~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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0]
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... U1
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6)), x3))), x7)) | is_a_theorem_1(x7) ....... R3 [R2:L0, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33
% 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(x3, x4)), equivalent_2(equivalent_2(x5, x0), equivalent_2(x5, x1))))) ....... R4 [R3:L0, U33:L0]
% Derivation of unit clause U170:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% ~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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | ~is_a_theorem_1(equivalent_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B3:L0]
% 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(x3,x4)),equivalent_2(equivalent_2(x5,x0),equivalent_2(x5,x1))))) ....... U104
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x5, x6), equivalent_2(x5, x7)), equivalent_2(x6, x7)), x4)))), x8)) | is_a_theorem_1(x8) ....... R3 [R2:L0, U104:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), equivalent_2(x2, x1))))) ....... R4 [R3:L0, U33:L0]
% Derivation of unit clause U574:
% is_a_theorem_1(equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1,x2),equivalent_2(x1,x3)),equivalent_2(x2,x3)),x0))) ....... 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(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B3:L0]
% ~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(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(equivalent_2(x2, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3, x4), equivalent_2(x3, x5)), equivalent_2(x4, x5)), x2)), x0))) ....... R2 [R1:L0, B3:L2]
% ~is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x0,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U103
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x3, x4)), x1)), equivalent_2(equivalent_2(x5, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x5, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R3 [R2:L0, U103:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x2)),equivalent_2(x1,x2))) ....... U33
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x2)), equivalent_2(x1, x2)), equivalent_2(equivalent_2(x3, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4, x5), equivalent_2(x4, x6)), equivalent_2(x5, x6)), x3)), equivalent_2(equivalent_2(x7, equivalent_2(equivalent_2(a_0(), b_0()), c_0())), equivalent_2(x7, equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R4 [R3:L0, U33: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(x1,x2)),equivalent_2(equivalent_2(x3,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x4,x5),equivalent_2(x4,x6)),equivalent_2(x5,x6)),x3)),equivalent_2(equivalent_2(x7,equivalent_2(equivalent_2(a_0(),b_0()),c_0())),equivalent_2(x7,equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))))) ....... U574
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(equivalent_2(equivalent_2(equivalent_2(x3,x4),equivalent_2(x3,x5)),equivalent_2(x4,x5)),equivalent_2(x2,x1))))) ....... U170
% [] ....... R1 [U574:L0, U170:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 89576
% resolvents: 89565 factors: 11
% Number of unit clauses generated: 88361
% % unit clauses generated to total clauses generated: 98.64
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 44 [4] = 528
% Total = 575
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 88361 [2] = 1196 [3] = 19
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)89 (-)486
% ------------------
% Total: (+)89 (-)486
% Total number of unit clauses retained: 575
% Number of clauses skipped because of their length: 1066
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 89596
% Number of unification failures: 109103
% Number of unit to unit unification failures: 43187
% N literal unification failure due to lookup root_id table: 36
% 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: 19
% N unit clauses dropped because they exceeded max values: 87520
% 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: 63
% Max term depth in a unit clause: 11
% Number of states in UCFA table: 11839
% Total number of terms of all unit clauses in table: 30973
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.02
% Ratio n states used/total unit clauses terms: 0.38
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 198699
% ConstructUnitClause() = 88092
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.42 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 89576
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 1.19 secs
%
%------------------------------------------------------------------------------