TSTP Solution File: GRP123-3.003 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : GRP123-3.003 : TPTP v5.0.0. Released v1.2.0.
% 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 20:51:05 EST 2010
% Result : Unsatisfiable 3.88s
% Output : Refutation 3.88s
% 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/SystemOnTPTP340/GRP/GRP123-3.003+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 = 40] [nf = 0] [nu = 0] [ut = 20]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 211] [nf = 8] [nu = 88] [ut = 40]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 385] [nf = 16] [nu = 176] [ut = 40]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 1443] [nf = 48] [nu = 552] [ut = 40]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 2501] [nf = 80] [nu = 928] [ut = 40]
% Looking for a proof at depth = 6 ...
% t = 0 secs [nr = 3559] [nf = 112] [nu = 1304] [ut = 40]
% Looking for a proof at depth = 7 ...
% t = 0 secs [nr = 4617] [nf = 144] [nu = 1680] [ut = 40]
% Looking for a proof at depth = 8 ...
% t = 0 secs [nr = 5675] [nf = 176] [nu = 2056] [ut = 40]
% Looking for a proof at depth = 9 ...
% t = 0 secs [nr = 6733] [nf = 208] [nu = 2432] [ut = 40]
% Looking for a proof at depth = 10 ...
% t = 0 secs [nr = 7791] [nf = 240] [nu = 2808] [ut = 40]
% Looking for a proof at depth = 11 ...
% t = 0 secs [nr = 8849] [nf = 272] [nu = 3184] [ut = 40]
% Looking for a proof at depth = 12 ...
% t = 0 secs [nr = 9907] [nf = 304] [nu = 3560] [ut = 40]
% Looking for a proof at depth = 13 ...
% t = 0 secs [nr = 10965] [nf = 336] [nu = 3936] [ut = 40]
% Looking for a proof at depth = 14 ...
% t = 0 secs [nr = 12023] [nf = 368] [nu = 4312] [ut = 40]
% Looking for a proof at depth = 15 ...
% t = 0 secs [nr = 13081] [nf = 400] [nu = 4688] [ut = 40]
% Looking for a proof at depth = 16 ...
% t = 0 secs [nr = 14139] [nf = 432] [nu = 5064] [ut = 40]
% Looking for a proof at depth = 17 ...
% t = 0 secs [nr = 15197] [nf = 464] [nu = 5440] [ut = 40]
% Looking for a proof at depth = 18 ...
% t = 0 secs [nr = 16255] [nf = 496] [nu = 5816] [ut = 40]
% Looking for a proof at depth = 19 ...
% t = 0 secs [nr = 17313] [nf = 528] [nu = 6192] [ut = 40]
% Looking for a proof at depth = 20 ...
% t = 0 secs [nr = 18371] [nf = 560] [nu = 6568] [ut = 40]
% Looking for a proof at depth = 21 ...
% t = 0 secs [nr = 19429] [nf = 592] [nu = 6944] [ut = 40]
% Looking for a proof at depth = 22 ...
% t = 0 secs [nr = 20487] [nf = 624] [nu = 7320] [ut = 40]
% Looking for a proof at depth = 23 ...
% t = 0 secs [nr = 21545] [nf = 656] [nu = 7696] [ut = 40]
% Looking for a proof at depth = 24 ...
% t = 0 secs [nr = 22603] [nf = 688] [nu = 8072] [ut = 40]
% Looking for a proof at depth = 25 ...
% t = 0 secs [nr = 23661] [nf = 720] [nu = 8448] [ut = 40]
% Looking for a proof at depth = 26 ...
% t = 0 secs [nr = 24719] [nf = 752] [nu = 8824] [ut = 40]
% Looking for a proof at depth = 27 ...
% t = 0 secs [nr = 25777] [nf = 784] [nu = 9200] [ut = 40]
% Looking for a proof at depth = 28 ...
% t = 0 secs [nr = 26835] [nf = 816] [nu = 9576] [ut = 40]
% Looking for a proof at depth = 29 ...
% t = 0 secs [nr = 27893] [nf = 848] [nu = 9952] [ut = 40]
% Looking for a proof at depth = 30 ...
% t = 0 secs [nr = 28951] [nf = 880] [nu = 10328] [ut = 40]
% Restarting search with different parameters.
% Looking for a proof at depth = 1 ...
% t = 0 secs [nr = 28991] [nf = 880] [nu = 10328] [ut = 40]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 29162] [nf = 888] [nu = 10416] [ut = 40]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 29356] [nf = 896] [nu = 10504] [ut = 40]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 31644] [nf = 1036] [nu = 11316] [ut = 52]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 50815] [nf = 1230] [nu = 18678] [ut = 59]
% Looking for a proof at depth = 6 ...
% t = 1 secs [nr = 276854] [nf = 2922] [nu = 109336] [ut = 64]
% Looking for a proof at depth = 7 ...
% t = 4 secs [nr = 1298493] [nf = 198170] [nu = 223132] [ut = 67]
% Looking for a proof at depth = 8 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~product_3(x5,x4,x3) | ~product_3(x5,x1,x0) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3)
% B2: product_3(x0,x0,x0)
% B3: group_element_1(e_1_0())
% B4: group_element_1(e_2_0())
% B22: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3)
% B23: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3)
% B24: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3)
% B29: ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0())
% Unit Clauses:
% --------------
% U1: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_1_0())
% U2: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0())
% U3: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_3_0())
% U5: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0())
% U7: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0())
% U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0())
% U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0())
% U10: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0())
% U23: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_2_0())
% U25: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_3_0())
% U29: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0())
% U30: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_3_0())
% U33: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0())
% U38: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_2_0())
% U46: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_3_0())
% U49: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_3_0(),e_2_0(),e_1_0())
% U67: < d8 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_1_0(),e_3_0())
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% group_element_1(e_1_0()) ....... U1
% Derivation of unit clause U2:
% group_element_1(e_2_0()) ....... U2
% Derivation of unit clause U3:
% group_element_1(e_3_0()) ....... U3
% Derivation of unit clause U5:
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% Derivation of unit clause U7:
% ~equalish_2(e_2_0(),e_1_0()) ....... U7
% Derivation of unit clause U8:
% ~equalish_2(e_2_0(),e_3_0()) ....... U8
% Derivation of unit clause U9:
% ~equalish_2(e_3_0(),e_1_0()) ....... U9
% Derivation of unit clause U10:
% ~equalish_2(e_3_0(),e_2_0()) ....... U10
% Derivation of unit clause U23:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B22
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B22:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U7
% ~product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U7:L0]
% Derivation of unit clause U25:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B22
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B22:L0]
% ~equalish_2(e_3_0(),e_1_0()) ....... U9
% ~product_3(e_1_0(), e_1_0(), e_3_0()) ....... R2 [R1:L1, U9:L0]
% Derivation of unit clause U29:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B23:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U7
% ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U7:L0]
% Derivation of unit clause U30:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B23
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B23:L0]
% ~equalish_2(e_2_0(),e_3_0()) ....... U8
% ~product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U8:L0]
% Derivation of unit clause U33:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B24:L0]
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U38:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B24
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B24:L0]
% ~equalish_2(e_3_0(),e_2_0()) ....... U10
% ~product_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U10:L0]
% Derivation of unit clause U46:
% group_element_1(e_1_0()) ....... B3
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29
% ~group_element_1(x0) | product_3(e_1_0(), x0, e_1_0()) | product_3(e_1_0(), x0, e_2_0()) | product_3(e_1_0(), x0, e_3_0()) ....... R1 [B3:L0, B29:L1]
% group_element_1(e_2_0()) ....... U2
% product_3(e_1_0(), e_2_0(), e_1_0()) | product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U2:L0]
% ~product_3(e_1_0(),e_2_0(),e_1_0()) ....... U29
% product_3(e_1_0(), e_2_0(), e_2_0()) | product_3(e_1_0(), e_2_0(), e_3_0()) ....... R3 [R2:L0, U29:L0]
% ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U33
% product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U33:L0]
% Derivation of unit clause U49:
% group_element_1(e_2_0()) ....... B4
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29
% ~group_element_1(x0) | product_3(x0, e_2_0(), e_1_0()) | product_3(x0, e_2_0(), e_2_0()) | product_3(x0, e_2_0(), e_3_0()) ....... R1 [B4:L0, B29:L0]
% group_element_1(e_3_0()) ....... U3
% product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_2_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U3:L0]
% ~product_3(e_3_0(),e_2_0(),e_2_0()) ....... U38
% product_3(e_3_0(), e_2_0(), e_1_0()) | product_3(e_3_0(), e_2_0(), e_3_0()) ....... R3 [R2:L1, U38:L0]
% ~product_3(e_3_0(),e_2_0(),e_3_0()) ....... U30
% product_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U30:L0]
% Derivation of unit clause U67:
% ~product_3(x5,x4,x3) | ~product_3(x5,x1,x0) | ~product_3(x3,x4,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B0
% ~product_3(x0, x1, x0) | ~product_3(x0, x2, x3) | ~product_3(x3, x2, x0) | equalish_2(x3, x0) ....... R1 [B0:L0, B0:L2]
% ~group_element_1(x1) | ~group_element_1(x0) | product_3(x0,x1,e_1_0()) | product_3(x0,x1,e_2_0()) | product_3(x0,x1,e_3_0()) ....... B29
% ~product_3(e_1_0(), x0, x1) | ~product_3(x1, x0, e_1_0()) | equalish_2(x1, e_1_0()) | ~group_element_1(x2) | ~group_element_1(e_1_0()) | product_3(e_1_0(), x2, e_2_0()) | product_3(e_1_0(), x2, e_3_0()) ....... R2 [R1:L0, B29:L2]
% ~product_3(e_1_0(), x0, x1) | ~product_3(x1, x0, e_1_0()) | equalish_2(x1, e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R3 [R2:L4, R2:L3]
% product_3(e_1_0(),e_2_0(),e_3_0()) ....... U46
% ~product_3(e_3_0(), e_2_0(), e_1_0()) | equalish_2(e_3_0(), e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R4 [R3:L0, U46:L0]
% product_3(e_3_0(),e_2_0(),e_1_0()) ....... U49
% equalish_2(e_3_0(), e_1_0()) | ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R5 [R4:L0, U49:L0]
% ~equalish_2(e_3_0(),e_1_0()) ....... U9
% ~group_element_1(e_1_0()) | product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R6 [R5:L0, U9:L0]
% group_element_1(e_1_0()) ....... U1
% product_3(e_1_0(), e_1_0(), e_2_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R7 [R6:L0, U1:L0]
% ~product_3(e_1_0(),e_1_0(),e_2_0()) ....... U23
% product_3(e_1_0(), e_1_0(), e_3_0()) ....... R8 [R7:L0, U23:L0]
% Derivation of the empty clause:
% product_3(e_1_0(),e_1_0(),e_3_0()) ....... U67
% ~product_3(e_1_0(),e_1_0(),e_3_0()) ....... U25
% [] ....... R1 [U67:L0, U25:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 1518233
% resolvents: 1320042 factors: 198191
% Number of unit clauses generated: 232421
% % unit clauses generated to total clauses generated: 15.31
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 20 [2] = 20 [4] = 12 [5] = 7 [6] = 5 [7] = 3
% [8] = 1
% Total = 68
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 232421 [2] = 320913 [3] = 638741 [4] = 292737 [5] = 19823 [6] = 12466
% [7] = 1092 [8] = 40
% Average size of a generated clause: 3.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] group_element_1 (+)3 (-)0
% [1] cycle_2 (+)3 (-)7
% [2] equalish_2 (+)5 (-)6
% [3] greater_2 (+)6 (-)3
% [4] next_2 (+)3 (-)3
% [5] product_3 (+)11 (-)18
% ------------------
% Total: (+)31 (-)37
% Total number of unit clauses retained: 68
% Number of clauses skipped because of their length: 2118899
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 62641
% Number of successful unifications: 1518261
% Number of unification failures: 7976730
% Number of unit to unit unification failures: 262
% N literal unification failure due to lookup root_id table: 1151677
% N base clause resolution failure due to lookup table: 771043
% N UC-BCL resolution dropped due to lookup table: 174334
% Max entries in substitution set: 11
% N unit clauses dropped because they exceeded max values: 115093
% 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: 3
% Max term depth in a unit clause: 1
% Number of states in UCFA table: 65
% Total number of terms of all unit clauses in table: 162
% Max allowed number of states in UCFA: 80000
% Ratio n states used/total allowed states: 0.00
% Ratio n states used/total unit clauses terms: 0.40
% Number of symbols (columns) in UCFA: 44
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 9494991
% ConstructUnitClause() = 115141
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.20 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 506078
% | |
% --------------------------------------------------------
% Elapsed time: 4 secs
% CPU time: 3.88 secs
%
%------------------------------------------------------------------------------