TSTP Solution File: LCL104-1 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL104-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Nov 28 00:02:21 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/SystemOnTPTP21018/LCL/LCL104-1+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 = 265] [nf = 0] [nu = 140] [ut = 86]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 693] [nf = 7] [nu = 434] [ut = 86]
% 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(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2))
% B3: ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(x0,x1)) | is_a_theorem_1(x1)
% Unit Clauses:
% --------------
% U2: < d0 v6 dv3 f5 c0 t11 td5 b > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2))
% U7: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))))
% U8: < d2 v10 dv5 f9 c0 t19 td7 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x3,x4)),x1))))
% U18: < 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(x3,x4),equivalent_2(equivalent_2(x5,x3),equivalent_2(x5,x4)))))
% U34: < d2 v8 dv4 f7 c0 t15 td6 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(x0,x3)))
% U53: < d2 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2)))))
% U130: < d4 v6 dv3 f13 c8 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0())))))
% U534: < d4 v8 dv4 f7 c0 t15 td5 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,equivalent_2(x3,x0)),equivalent_2(x2,equivalent_2(x3,x1)))))
% --------------- Start of Proof ---------------
% Derivation of unit clause U2:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... 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(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1)))) ....... R2 [R1:L0, U2:L0]
% Derivation of unit clause U8:
% 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(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2, x3), equivalent_2(x2, x4)), equivalent_2(x3, x4)), x1)))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U18:
% 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(x0) | is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x1, x2), equivalent_2(x1, x3)), equivalent_2(x2, x3)), x0)) ....... R1 [B1:L0, B3:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U7
% 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, x4), equivalent_2(equivalent_2(x5, x3), equivalent_2(x5, x4))))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U34:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... 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(equivalent_2(x1, x0), x2)), x2), x3)) | is_a_theorem_1(x3) ....... R1 [B2:L0, B3:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1)))) ....... U7
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x2, x1), x3))), equivalent_2(x0, x3))) ....... R2 [R1:L0, U7:L0]
% Derivation of unit clause U53:
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... 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(x0, x1), equivalent_2(equivalent_2(x1, x0), x2))) | is_a_theorem_1(x2) ....... 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(x3,x4),equivalent_2(equivalent_2(x5,x3),equivalent_2(x5,x4))))) ....... U18
% is_a_theorem_1(equivalent_2(equivalent_2(x0, equivalent_2(x1, x2)), equivalent_2(x0, equivalent_2(equivalent_2(x3, x1), equivalent_2(x3, x2))))) ....... R2 [R1:L0, U18:L0]
% Derivation of unit clause U130:
% ~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(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()))))) | ~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(equivalent_2(x1,x2),equivalent_2(equivalent_2(x2,x1),x3))),equivalent_2(x0,x3))) ....... U34
% ~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(x1, x2), equivalent_2(equivalent_2(x2, x1), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))))) ....... R3 [R2:L0, U34:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,equivalent_2(equivalent_2(equivalent_2(equivalent_2(x2,x3),equivalent_2(x2,x4)),equivalent_2(x3,x4)),x1)))) ....... U8
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(), b_0()), c_0()), equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), equivalent_2(equivalent_2(e_0(), b_0()), equivalent_2(equivalent_2(a_0(), e_0()), c_0()))))) ....... R4 [R3:L1, U8:L0]
% Derivation of unit clause U534:
% 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(equivalent_2(x0,x1),equivalent_2(equivalent_2(x1,x0),x2)),x2)) ....... U2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, x0), equivalent_2(x2, x1))), x3)) | is_a_theorem_1(x3) ....... R3 [R2:L0, U2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(x1,x2)),equivalent_2(x0,equivalent_2(equivalent_2(x3,x1),equivalent_2(x3,x2))))) ....... U53
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x2, equivalent_2(x3, x0)), equivalent_2(x2, equivalent_2(x3, x1))))) ....... R4 [R3:L0, U53:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,equivalent_2(x3,x0)),equivalent_2(x2,equivalent_2(x3,x1))))) ....... U534
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(a_0(),b_0()),c_0()),equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x2,x0),equivalent_2(x2,x1))),equivalent_2(equivalent_2(e_0(),b_0()),equivalent_2(equivalent_2(a_0(),e_0()),c_0()))))) ....... U130
% [] ....... R1 [U534:L0, U130:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 4566
% resolvents: 4555 factors: 11
% Number of unit clauses generated: 4161
% % unit clauses generated to total clauses generated: 91.13
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 83 [4] = 449
% Total = 535
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 4161 [2] = 388 [3] = 17
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)33 (-)502
% ------------------
% Total: (+)33 (-)502
% Total number of unit clauses retained: 535
% 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: 4584
% Number of unification failures: 5691
% Number of unit to unit unification failures: 16165
% 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: 0
% Max entries in substitution set: 19
% N unit clauses dropped because they exceeded max values: 2839
% N unit clauses dropped because too much nesting: 45
% 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: 12
% Number of states in UCFA table: 12357
% Total number of terms of all unit clauses in table: 26353
% 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: 0.47
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 10275
% ConstructUnitClause() = 3371
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.02 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 0.40 secs
%
%------------------------------------------------------------------------------