TSTP Solution File: GRP123-1.003 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : GRP123-1.003 : TPTP v5.0.0. Released v1.2.0.
% 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 : Sat Nov 27 20:52:20 EST 2010
% Result : Unsatisfiable 3.50s
% Output : Refutation 3.50s
% 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/SystemOnTPTP12391/GRP/GRP123-1.003+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 = 24] [nf = 0] [nu = 0] [ut = 10]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 156] [nf = 6] [nu = 84] [ut = 29]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 288] [nf = 12] [nu = 168] [ut = 29]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 1304] [nf = 42] [nu = 540] [ut = 29]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 2320] [nf = 72] [nu = 912] [ut = 29]
% Looking for a proof at depth = 6 ...
% t = 0 secs [nr = 3336] [nf = 102] [nu = 1284] [ut = 29]
% Looking for a proof at depth = 7 ...
% t = 0 secs [nr = 4352] [nf = 132] [nu = 1656] [ut = 29]
% Looking for a proof at depth = 8 ...
% t = 0 secs [nr = 5368] [nf = 162] [nu = 2028] [ut = 29]
% Looking for a proof at depth = 9 ...
% t = 0 secs [nr = 6384] [nf = 192] [nu = 2400] [ut = 29]
% Looking for a proof at depth = 10 ...
% t = 0 secs [nr = 7400] [nf = 222] [nu = 2772] [ut = 29]
% Looking for a proof at depth = 11 ...
% t = 0 secs [nr = 8416] [nf = 252] [nu = 3144] [ut = 29]
% Looking for a proof at depth = 12 ...
% t = 0 secs [nr = 9432] [nf = 282] [nu = 3516] [ut = 29]
% Looking for a proof at depth = 13 ...
% t = 0 secs [nr = 10448] [nf = 312] [nu = 3888] [ut = 29]
% Looking for a proof at depth = 14 ...
% t = 0 secs [nr = 11464] [nf = 342] [nu = 4260] [ut = 29]
% Looking for a proof at depth = 15 ...
% t = 0 secs [nr = 12480] [nf = 372] [nu = 4632] [ut = 29]
% Looking for a proof at depth = 16 ...
% t = 0 secs [nr = 13496] [nf = 402] [nu = 5004] [ut = 29]
% Looking for a proof at depth = 17 ...
% t = 0 secs [nr = 14512] [nf = 432] [nu = 5376] [ut = 29]
% Looking for a proof at depth = 18 ...
% t = 0 secs [nr = 15528] [nf = 462] [nu = 5748] [ut = 29]
% Looking for a proof at depth = 19 ...
% t = 0 secs [nr = 16544] [nf = 492] [nu = 6120] [ut = 29]
% Looking for a proof at depth = 20 ...
% t = 0 secs [nr = 17560] [nf = 522] [nu = 6492] [ut = 29]
% Looking for a proof at depth = 21 ...
% t = 0 secs [nr = 18576] [nf = 552] [nu = 6864] [ut = 29]
% Looking for a proof at depth = 22 ...
% t = 0 secs [nr = 19592] [nf = 582] [nu = 7236] [ut = 29]
% Looking for a proof at depth = 23 ...
% t = 0 secs [nr = 20608] [nf = 612] [nu = 7608] [ut = 29]
% Looking for a proof at depth = 24 ...
% t = 0 secs [nr = 21624] [nf = 642] [nu = 7980] [ut = 29]
% Looking for a proof at depth = 25 ...
% t = 0 secs [nr = 22640] [nf = 672] [nu = 8352] [ut = 29]
% Looking for a proof at depth = 26 ...
% t = 0 secs [nr = 23656] [nf = 702] [nu = 8724] [ut = 29]
% Looking for a proof at depth = 27 ...
% t = 0 secs [nr = 24672] [nf = 732] [nu = 9096] [ut = 29]
% Looking for a proof at depth = 28 ...
% t = 0 secs [nr = 25688] [nf = 762] [nu = 9468] [ut = 29]
% Looking for a proof at depth = 29 ...
% t = 0 secs [nr = 26704] [nf = 792] [nu = 9840] [ut = 29]
% Looking for a proof at depth = 30 ...
% t = 0 secs [nr = 27720] [nf = 822] [nu = 10212] [ut = 29]
% Restarting search with different parameters.
% Looking for a proof at depth = 1 ...
% t = 0 secs [nr = 27744] [nf = 822] [nu = 10212] [ut = 29]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 27876] [nf = 828] [nu = 10296] [ut = 29]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 28014] [nf = 834] [nu = 10380] [ut = 29]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 29635] [nf = 866] [nu = 11058] [ut = 38]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 42934] [nf = 934] [nu = 17646] [ut = 38]
% Looking for a proof at depth = 6 ...
% t = 1 secs [nr = 255165] [nf = 1002] [nu = 105746] [ut = 41]
% Looking for a proof at depth = 7 ...
% t = 3 secs [nr = 1130372] [nf = 193234] [nu = 193846] [ut = 41]
% 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())
% B12: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3)
% B13: ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3)
% B14: ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3)
% B15: ~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())
% U4: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0())
% U6: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_1_0())
% U7: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_2_0(),e_3_0())
% U8: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_1_0())
% U9: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0())
% U13: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_2_0())
% U15: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_3_0())
% U19: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0())
% U20: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_3_0())
% U23: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0())
% U28: < d2 v0 dv0 f0 c3 t3 td1 > ~product_3(e_3_0(),e_2_0(),e_2_0())
% U32: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_3_0())
% U35: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_3_0(),e_2_0(),e_1_0())
% U41: < 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 U4:
% ~equalish_2(e_1_0(),e_2_0()) ....... U4
% Derivation of unit clause U6:
% ~equalish_2(e_2_0(),e_1_0()) ....... U6
% Derivation of unit clause U7:
% ~equalish_2(e_2_0(),e_3_0()) ....... U7
% Derivation of unit clause U8:
% ~equalish_2(e_3_0(),e_1_0()) ....... U8
% Derivation of unit clause U9:
% ~equalish_2(e_3_0(),e_2_0()) ....... U9
% Derivation of unit clause U13:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B12:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U6
% ~product_3(e_1_0(), e_1_0(), e_2_0()) ....... R2 [R1:L1, U6:L0]
% Derivation of unit clause U15:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R1 [B2:L0, B12:L0]
% ~equalish_2(e_3_0(),e_1_0()) ....... U8
% ~product_3(e_1_0(), e_1_0(), e_3_0()) ....... R2 [R1:L1, U8:L0]
% Derivation of unit clause U19:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B13:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U6
% ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U6:L0]
% Derivation of unit clause U20:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B2:L0, B13:L0]
% ~equalish_2(e_2_0(),e_3_0()) ....... U7
% ~product_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U7:L0]
% Derivation of unit clause U23:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B14:L0]
% ~equalish_2(e_1_0(),e_2_0()) ....... U4
% ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U4:L0]
% Derivation of unit clause U28:
% product_3(x0,x0,x0) ....... B2
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B2:L0, B14:L0]
% ~equalish_2(e_3_0(),e_2_0()) ....... U9
% ~product_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U9:L0]
% Derivation of unit clause U32:
% 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()) ....... B15
% ~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, B15: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()) ....... U19
% 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, U19:L0]
% ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U23
% product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U23:L0]
% Derivation of unit clause U35:
% 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()) ....... B15
% ~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, B15: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()) ....... U28
% 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, U28:L0]
% ~product_3(e_3_0(),e_2_0(),e_3_0()) ....... U20
% product_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U20:L0]
% Derivation of unit clause U41:
% ~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()) ....... B15
% ~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, B15: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()) ....... U32
% ~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, U32:L0]
% product_3(e_3_0(),e_2_0(),e_1_0()) ....... U35
% 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, U35:L0]
% ~equalish_2(e_3_0(),e_1_0()) ....... U8
% ~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, U8: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()) ....... U13
% product_3(e_1_0(), e_1_0(), e_3_0()) ....... R8 [R7:L0, U13:L0]
% Derivation of the empty clause:
% product_3(e_1_0(),e_1_0(),e_3_0()) ....... U41
% ~product_3(e_1_0(),e_1_0(),e_3_0()) ....... U15
% [] ....... R1 [U41:L0, U15:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 1345176
% resolvents: 1151921 factors: 193255
% Number of unit clauses generated: 203135
% % unit clauses generated to total clauses generated: 15.10
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 10 [2] = 19 [4] = 9 [6] = 3 [8] = 1
% Total = 42
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 203135 [2] = 270591 [3] = 576991 [4] = 275807 [5] = 9149 [6] = 8869
% [7] = 634
% Average size of a generated clause: 3.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] group_element_1 (+)3 (-)0
% [1] equalish_2 (+)4 (-)6
% [2] product_3 (+)11 (-)18
% ------------------
% Total: (+)18 (-)24
% Total number of unit clauses retained: 42
% Number of clauses skipped because of their length: 1223353
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 23460
% Number of successful unifications: 1345204
% Number of unification failures: 6913711
% Number of unit to unit unification failures: 208
% N literal unification failure due to lookup root_id table: 772776
% N base clause resolution failure due to lookup table: 346460
% N UC-BCL resolution dropped due to lookup table: 171976
% Max entries in substitution set: 11
% N unit clauses dropped because they exceeded max values: 91105
% 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: 41
% Total number of terms of all unit clauses in table: 110
% 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: 0.37
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 8258915
% ConstructUnitClause() = 91137
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.11 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 448392
% | |
% --------------------------------------------------------
% Elapsed time: 3 secs
% CPU time: 3.49 secs
%
%------------------------------------------------------------------------------