TSTP Solution File: LCL082-1 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL082-1 : 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 23:50:57 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/SystemOnTPTP22064/LCL/LCL082-1+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 = 38] [nf = 0] [nu = 13] [ut = 13]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 90] [nf = 4] [nu = 35] [ut = 13]
% 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(implies_2(a_0(),implies_2(b_0(),a_0())))
% B1: is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))))
% B2: ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U1: < d0 v7 dv4 f6 c0 t13 td4 b > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))))
% U2: < d2 v7 dv4 f9 c3 t19 td5 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(a_0(),implies_2(b_0(),a_0()))))
% U3: < d2 v9 dv5 f8 c0 t17 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))))
% U4: < d2 v14 dv8 f16 c3 t33 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(implies_2(implies_2(implies_2(x4,x5),x6),implies_2(implies_2(x6,x4),implies_2(x7,x4))),implies_2(a_0(),implies_2(b_0(),a_0())))))
% U6: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1)))))
% U107: < d4 v23 dv13 f25 c3 t51 td7 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))),implies_2(implies_2(implies_2(implies_2(x5,x6),x7),implies_2(implies_2(x7,x5),implies_2(x8,x5))),implies_2(implies_2(implies_2(implies_2(x9,x10),x11),implies_2(implies_2(x11,x9),implies_2(x12,x9))),implies_2(a_0(),implies_2(b_0(),a_0()))))))
% U166: < d4 v8 dv5 f7 c0 t15 td6 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),x3),implies_2(x4,x3)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1
% Derivation of unit clause U2:
% ~is_a_theorem_1(implies_2(a_0(),implies_2(b_0(),a_0()))) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R1 [B0:L0, B2:L2]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(a_0(), implies_2(b_0(), a_0())))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U3:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3)))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U4:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(a_0(),implies_2(b_0(),a_0())))) ....... U2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), implies_2(implies_2(implies_2(implies_2(x4, x5), x6), implies_2(implies_2(x6, x4), implies_2(x7, x4))), implies_2(a_0(), implies_2(b_0(), a_0()))))) ....... R2 [R1:L1, U2:L0]
% Derivation of unit clause U6:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(x0, x1), x2)) | is_a_theorem_1(implies_2(implies_2(x2, x0), implies_2(x3, x0))) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3)))) ....... U3
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(implies_2(x3, x1), implies_2(x4, x1))), implies_2(x5, implies_2(implies_2(x3, x1), implies_2(x4, x1))))) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U107:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | ~is_a_theorem_1(implies_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3))), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U1:L0]
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0))),implies_2(implies_2(implies_2(implies_2(x4,x5),x6),implies_2(implies_2(x6,x4),implies_2(x7,x4))),implies_2(a_0(),implies_2(b_0(),a_0()))))) ....... U4
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), implies_2(x2, x1)), implies_2(x1, x3)), implies_2(x4, implies_2(x1, x3))), implies_2(implies_2(implies_2(implies_2(x5, x6), x7), implies_2(implies_2(x7, x5), implies_2(x8, x5))), implies_2(implies_2(implies_2(implies_2(x9, x10), x11), implies_2(implies_2(x11, x9), implies_2(x12, x9))), implies_2(a_0(), implies_2(b_0(), a_0())))))) ....... R4 [R3:L1, U4:L0]
% Derivation of unit clause U166:
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... B1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B2
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x2), implies_2(implies_2(x2, x0), implies_2(x3, x0))), x4)) | ~is_a_theorem_1(implies_2(x4, x5)) | is_a_theorem_1(x5) ....... R2 [R1:L1, B2:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(implies_2(x3,x1),implies_2(x4,x1))),implies_2(x5,implies_2(implies_2(x3,x1),implies_2(x4,x1))))) ....... U6
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(x1, x2), x1), implies_2(x3, x1))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U6:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x2),implies_2(implies_2(x2,x0),implies_2(x3,x0)))) ....... U1
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), x3), implies_2(x4, x3))) ....... R4 [R3:L0, U1:L0]
% Derivation of the empty clause:
% is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),x3),implies_2(x4,x3))) ....... U166
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),implies_2(x2,x1)),implies_2(x1,x3)),implies_2(x4,implies_2(x1,x3))),implies_2(implies_2(implies_2(implies_2(x5,x6),x7),implies_2(implies_2(x7,x5),implies_2(x8,x5))),implies_2(implies_2(implies_2(implies_2(x9,x10),x11),implies_2(implies_2(x11,x9),implies_2(x12,x9))),implies_2(a_0(),implies_2(b_0(),a_0())))))) ....... U107
% [] ....... R1 [U166:L0, U107:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 520
% resolvents: 512 factors: 8
% Number of unit clauses generated: 414
% % unit clauses generated to total clauses generated: 79.62
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 11 [4] = 154
% Total = 167
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 414 [2] = 95 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)19 (-)148
% ------------------
% Total: (+)19 (-)148
% Total number of unit clauses retained: 167
% Number of clauses skipped because of their length: 52
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 536
% Number of unification failures: 789
% Number of unit to unit unification failures: 2753
% 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: 18
% N unit clauses dropped because they exceeded max values: 163
% 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: 10
% Number of states in UCFA table: 2819
% Total number of terms of all unit clauses in table: 6873
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.01
% Ratio n states used/total unit clauses terms: 0.41
% Number of symbols (columns) in UCFA: 38
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 1325
% ConstructUnitClause() = 328
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.35 secs
%
%------------------------------------------------------------------------------