TSTP Solution File: LCL083-2 by CARINE---0.734
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- Process Solution
%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL083-2 : TPTP v5.0.0. Bugfixed v1.2.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art03.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 23:54:33 EST 2010
% Result : Unsatisfiable 1.43s
% Output : Refutation 1.43s
% 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/SystemOnTPTP23855/LCL/LCL083-2+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 = 291] [nf = 0] [nu = 177] [ut = 82]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 715] [nf = 5] [nu = 478] [ut = 82]
% 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(implies_2(implies_2(a_0(),b_0()),a_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))))
% B3: ~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: < d0 v2 dv1 f1 c0 t3 td2 b > is_a_theorem_1(implies_2(x0,x0))
% U11: < d2 v5 dv3 f4 c0 t9 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)))
% U13: < d2 v7 dv4 f6 c0 t13 td4 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x1,x2))))
% U15: < d2 v8 dv5 f7 c0 t15 td5 > is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x1)),implies_2(x4,implies_2(x3,x1))))
% U236: < d4 v10 dv3 f13 c4 t27 td6 > ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))))
% U1139: < d4 v19 dv8 f22 c4 t45 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),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(implies_2(x5,x6),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))))
% U2475: < d4 v26 dv12 f29 c4 t59 td8 > ~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(implies_2(x4,x5),implies_2(x6,x5)),implies_2(x5,x7)),implies_2(x8,implies_2(x5,x7))),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))))))
% U4865: < d4 v9 dv5 f8 c0 t17 td7 > is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(implies_2(implies_2(x0,x1),x2),x1),implies_2(x0,x1)),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(x0,x0)) ....... U2
% Derivation of unit clause U11:
% 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) ....... B3
% ~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, B3:L1]
% is_a_theorem_1(implies_2(x0,x0)) ....... U2
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U13:
% 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) ....... B3
% ~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, B3:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) ....... U11
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, x1), implies_2(x1, x2)), implies_2(x3, implies_2(x1, x2)))) ....... R2 [R1:L0, U11:L0]
% Derivation of unit clause U15:
% 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) ....... B3
% ~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, B3:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),implies_2(x1,x2)),implies_2(x3,implies_2(x1,x2)))) ....... U13
% is_a_theorem_1(implies_2(implies_2(implies_2(x0, implies_2(x1, x2)), implies_2(x3, x1)), implies_2(x4, implies_2(x3, x1)))) ....... R2 [R1:L0, U13:L0]
% Derivation of unit clause U236:
% ~is_a_theorem_1(implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())) ....... B0
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))) ....... R1 [B0:L0, B3:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(implies_2(x1, implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R2 [R1:L1, B3:L2]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0, implies_2(x0, implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R3 [R2:L0, R2:L1]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0))) ....... U11
% ~is_a_theorem_1(implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), implies_2(implies_2(implies_2(implies_2(x0, x1), x0), implies_2(x2, x0)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))) ....... R4 [R3:L0, U11:L0]
% Derivation of unit clause U1139:
% 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) ....... B3
% ~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, B3:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~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, B3: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),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(implies_2(x0,x1),x0),implies_2(x2,x0)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))) ....... U236
% ~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), x5), implies_2(x7, x5)), implies_2(implies_2(implies_2(implies_2(x5, x6), x5), implies_2(x7, x5)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0()))))) ....... R4 [R3:L1, U236:L0]
% Derivation of unit clause U2475:
% 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) ....... B3
% ~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, B3:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~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, B3:L0]
% is_a_theorem_1(implies_2(x0,x0)) ....... 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))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U2:L0]
% ~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),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(implies_2(x5,x6),x5),implies_2(x7,x5)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0()))))) ....... U1139
% ~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(implies_2(x4, x5), implies_2(x6, x5)), implies_2(x5, x7)), implies_2(x8, implies_2(x5, x7))), implies_2(implies_2(implies_2(implies_2(x9, x10), x9), implies_2(x11, x9)), implies_2(implies_2(implies_2(implies_2(x9, x10), x9), implies_2(x11, x9)), implies_2(implies_2(implies_2(a_0(), b_0()), a_0()), a_0())))))) ....... R4 [R3:L1, U1139:L0]
% Derivation of unit clause U4865:
% 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) ....... B3
% ~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, B3:L0]
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(implies_2(x0,x1)) | is_a_theorem_1(x1) ....... B3
% ~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, B3:L0]
% is_a_theorem_1(implies_2(implies_2(implies_2(x0,implies_2(x1,x2)),implies_2(x3,x1)),implies_2(x4,implies_2(x3,x1)))) ....... U15
% ~is_a_theorem_1(implies_2(implies_2(x0, implies_2(implies_2(implies_2(implies_2(x1, x2), x3), x2), implies_2(x1, x2))), x4)) | is_a_theorem_1(x4) ....... R3 [R2:L0, U15: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(implies_2(x0, x1), x2), x1), implies_2(x0, x1)), 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(implies_2(x0,x1),x2),x1),implies_2(x0,x1)),x3),implies_2(x4,x3))) ....... U4865
% ~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(implies_2(x4,x5),implies_2(x6,x5)),implies_2(x5,x7)),implies_2(x8,implies_2(x5,x7))),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(implies_2(x9,x10),x9),implies_2(x11,x9)),implies_2(implies_2(implies_2(a_0(),b_0()),a_0()),a_0())))))) ....... U2475
% [] ....... R1 [U4865:L0, U2475:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 9180
% resolvents: 9171 factors: 9
% Number of unit clauses generated: 8799
% % unit clauses generated to total clauses generated: 95.85
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 79 [4] = 4784
% Total = 4866
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 8799 [2] = 364 [3] = 17
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)114 (-)4752
% ------------------
% Total: (+)114 (-)4752
% Total number of unit clauses retained: 4866
% Number of clauses skipped because of their length: 152
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 9202
% Number of unification failures: 11491
% Number of unit to unit unification failures: 539374
% N literal unification failure due to lookup root_id table: 35
% N base clause resolution failure due to lookup table: 0
% N UC-BCL resolution dropped due to lookup table: 11
% Max entries in substitution set: 19
% N unit clauses dropped because they exceeded max values: 2941
% N unit clauses dropped because too much nesting: 224
% 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: 58934
% Total number of terms of all unit clauses in table: 230368
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.11
% Ratio n states used/total unit clauses terms: 0.26
% Number of symbols (columns) in UCFA: 38
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 20693
% ConstructUnitClause() = 7804
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.04 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 9180
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 1.42 secs
%
%------------------------------------------------------------------------------