TSTP Solution File: LCL130-1 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : LCL130-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art07.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 00:09:04 EST 2010
% Result : Unsatisfiable 0.37s
% Output : Refutation 0.37s
% 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/SystemOnTPTP25758/LCL/LCL130-1+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 = 3] [nf = 0] [nu = 0] [ut = 2]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 52] [nf = 0] [nu = 26] [ut = 17]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 119] [nf = 5] [nu = 62] [ut = 17]
% 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(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0()))))))
% B1: is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0))
% B2: ~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(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0))
% U4: < d2 v12 dv6 f11 c0 t23 td5 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5)))))
% U9: < d2 v6 dv3 f5 c0 t11 td4 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))))
% U38: < d4 v6 dv3 f13 c8 t27 td6 > ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0()))))))
% U50: < d4 v12 dv6 f11 c0 t23 td8 > is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(equivalent_2(x0,x4),x5)))
% U53: < d4 v4 dv2 f3 c0 t7 td3 > is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1)))
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1
% Derivation of unit clause U4:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(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) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... R1 [B1:L0, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2))), equivalent_2(equivalent_2(x3, x4), equivalent_2(equivalent_2(x3, x5), equivalent_2(x4, x5))))) ....... R2 [R1:L0, U1:L0]
% Derivation of unit clause U9:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(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) ....... B2
% ~is_a_theorem_1(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3))))) | is_a_theorem_1(x0) ....... R1 [B1:L0, B2:L1]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2))),equivalent_2(equivalent_2(x3,x4),equivalent_2(equivalent_2(x3,x5),equivalent_2(x4,x5))))) ....... U4
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2)))) ....... R2 [R1:L0, U4:L0]
% Derivation of unit clause U38:
% ~is_a_theorem_1(equivalent_2(a_0(),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_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(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_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(x0) | ~is_a_theorem_1(x1) | ~is_a_theorem_1(equivalent_2(x1, equivalent_2(x0, equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))))) ....... R2 [R1:L1, B2:L2]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x0)) ....... U1
% ~is_a_theorem_1(x0) | ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x1, equivalent_2(equivalent_2(x2, x3), equivalent_2(equivalent_2(x2, x4), equivalent_2(x3, x4)))), x1), equivalent_2(x0, equivalent_2(a_0(), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))))) ....... R3 [R2:L1, U1:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9
% ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(), equivalent_2(equivalent_2(x0, x1), equivalent_2(equivalent_2(x0, x2), equivalent_2(x1, x2)))), equivalent_2(a_0(), equivalent_2(equivalent_2(b_0(), c_0()), equivalent_2(equivalent_2(b_0(), e_0()), equivalent_2(c_0(), e_0())))))) ....... R4 [R3:L1, U9:L0]
% Derivation of unit clause U50:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(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) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(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, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), equivalent_2(x0, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U9:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), x5), equivalent_2(equivalent_2(x0, x4), x5))) ....... R4 [R3:L0, U9:L0]
% Derivation of unit clause U53:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(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) ....... B2
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x0), x4)) | is_a_theorem_1(x4) ....... 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, equivalent_2(equivalent_2(x1, x2), equivalent_2(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, B2:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))) ....... U9
% ~is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0, equivalent_2(equivalent_2(x1, x2), equivalent_2(equivalent_2(x1, x3), equivalent_2(x2, x3)))), x4), equivalent_2(x0, x4)), x5)) | is_a_theorem_1(x5) ....... R3 [R2:L0, U9:L0]
% is_a_theorem_1(equivalent_2(equivalent_2(equivalent_2(equivalent_2(x0,equivalent_2(equivalent_2(x1,x2),equivalent_2(equivalent_2(x1,x3),equivalent_2(x2,x3)))),x4),x5),equivalent_2(equivalent_2(x0,x4),x5))) ....... U50
% is_a_theorem_1(equivalent_2(equivalent_2(x0, x1), equivalent_2(x0, x1))) ....... R4 [R3:L0, U50:L0]
% Derivation of the empty clause:
% is_a_theorem_1(equivalent_2(equivalent_2(x0,x1),equivalent_2(x0,x1))) ....... U53
% ~is_a_theorem_1(equivalent_2(equivalent_2(a_0(),equivalent_2(equivalent_2(x0,x1),equivalent_2(equivalent_2(x0,x2),equivalent_2(x1,x2)))),equivalent_2(a_0(),equivalent_2(equivalent_2(b_0(),c_0()),equivalent_2(equivalent_2(b_0(),e_0()),equivalent_2(c_0(),e_0())))))) ....... U38
% [] ....... R1 [U53:L0, U38:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 297
% resolvents: 288 factors: 9
% Number of unit clauses generated: 209
% % unit clauses generated to total clauses generated: 70.37
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 2 [2] = 15 [4] = 37
% Total = 54
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 209 [2] = 77 [3] = 11
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] is_a_theorem_1 (+)9 (-)45
% ------------------
% Total: (+)9 (-)45
% Total number of unit clauses retained: 54
% Number of clauses skipped because of their length: 31
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 313
% Number of unification failures: 136
% Number of unit to unit unification failures: 395
% 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: 79
% 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: 1436
% Total number of terms of all unit clauses in table: 2326
% Max allowed number of states in UCFA: 528000
% Ratio n states used/total allowed states: 0.00
% Ratio n states used/total unit clauses terms: 0.62
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 449
% ConstructUnitClause() = 131
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 1 secs
% CPU time: 0.36 secs
%
%------------------------------------------------------------------------------