TSTP Solution File: GRP128-4.003 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : GRP128-4.003 : TPTP v5.0.0. Bugfixed v1.2.1.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art09.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 21:21:34 EST 2010
% Result : Unsatisfiable 31.01s
% Output : Refutation 31.01s
% 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/SystemOnTPTP8741/GRP/GRP128-4.003+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 = 18] [nf = 0] [nu = 0] [ut = 9]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 54] [nf = 12] [nu = 0] [ut = 9]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 306] [nf = 528] [nu = 0] [ut = 9]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 1026] [nf = 1044] [nu = 108] [ut = 27]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 7956] [nf = 12792] [nu = 252] [ut = 27]
% Looking for a proof at depth = 6 ...
% t = 0 secs [nr = 21942] [nf = 24540] [nu = 1260] [ut = 27]
% Looking for a proof at depth = 7 ...
% t = 1 secs [nr = 145656] [nf = 218592] [nu = 2268] [ut = 27]
% Looking for a proof at depth = 8 ...
% t = 1 secs [nr = 348570] [nf = 412644] [nu = 14220] [ut = 27]
% Looking for a proof at depth = 9 ...
% t = 8 secs [nr = 2117052] [nf = 3196392] [nu = 26172] [ut = 27]
% Looking for a proof at depth = 10 ...
% t = 19 secs [nr = 4836510] [nf = 5980140] [nu = 165996] [ut = 27]
% Looking for a proof at depth = 11 ...
% Entering time slice 2
% Updating parameters ... done.
% Looking for a proof at depth = 1 ...
% t = 31 secs [nr = 7858422] [nf = 10738026] [nu = 187494] [ut = 27]
% Looking for a proof at depth = 2 ...
% t = 31 secs [nr = 7858512] [nf = 10738038] [nu = 187494] [ut = 27]
% Looking for a proof at depth = 3 ...
% t = 31 secs [nr = 7858878] [nf = 10738662] [nu = 187494] [ut = 27]
% Looking for a proof at depth = 4 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~product_3(x2,x1,x3) | ~product_3(x0,x2,x3) | product_3(x0,x1,x2)
% B1: ~product_3(x3,x1,x0) | ~product_3(x3,x0,x2) | product_3(x0,x1,x2)
% B2: ~product_3(x2,x1,x3) | ~product_3(x0,x1,x2) | product_3(x0,x2,x3)
% B3: group_element_1(e_1_0())
% B6: ~equalish_2(e_1_0(),e_2_0())
% B12: ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,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:
% --------------
% U0: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_1_0())
% U1: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0())
% U3: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_1_0(),e_2_0())
% U5: < 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_3_0(),e_1_0())
% U11: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_2_0())
% U13: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_1_0(),e_3_0())
% U15: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_2_0())
% U17: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_1_0())
% U21: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_2_0(),e_1_0(),e_2_0())
% U23: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_1_0())
% U27: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_1_0(),e_1_0())
% U28: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_2_0(),e_1_0(),e_3_0())
% U30: < d4 v0 dv0 f0 c3 t3 td1 > product_3(e_1_0(),e_2_0(),e_3_0())
% U36: < d4 v0 dv0 f0 c3 t3 td1 > ~product_3(e_1_0(),e_2_0(),e_3_0())
% --------------- Start of Proof ---------------
% Derivation of unit clause U0:
% group_element_1(e_1_0()) ....... U0
% Derivation of unit clause U1:
% group_element_1(e_2_0()) ....... U1
% Derivation of unit clause U3:
% ~equalish_2(e_1_0(),e_2_0()) ....... U3
% Derivation of unit clause U5:
% ~equalish_2(e_2_0(),e_1_0()) ....... U5
% Derivation of unit clause U7:
% ~equalish_2(e_3_0(),e_1_0()) ....... U7
% Derivation of unit clause U11:
% ~product_3(x2,x1,x3) | ~product_3(x0,x2,x3) | product_3(x0,x1,x2) ....... B0
% ~product_3(x0, x0, x1) | product_3(x0, x0, x0) ....... R1 [B0:L0, B0:L1]
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12
% ~product_3(x0, x0, x1) | ~product_3(x0, x0, x2) | equalish_2(x2, x0) ....... R2 [R1:L1, B12:L0]
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_2_0(),e_1_0()) ....... U5
% ~product_3(e_1_0(), e_1_0(), e_2_0()) ....... R4 [R3:L1, U5:L0]
% Derivation of unit clause U13:
% ~product_3(x2,x1,x3) | ~product_3(x0,x2,x3) | product_3(x0,x1,x2) ....... B0
% ~product_3(x0, x0, x1) | product_3(x0, x0, x0) ....... R1 [B0:L0, B0:L1]
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12
% ~product_3(x0, x0, x1) | ~product_3(x0, x0, x2) | equalish_2(x2, x0) ....... R2 [R1:L1, B12:L0]
% ~product_3(x0, x0, x1) | equalish_2(x1, x0) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_3_0(),e_1_0()) ....... U7
% ~product_3(e_1_0(), e_1_0(), e_3_0()) ....... R4 [R3:L1, U7:L0]
% Derivation of unit clause U15:
% ~product_3(x3,x1,x0) | ~product_3(x3,x0,x2) | product_3(x0,x1,x2) ....... B1
% ~product_3(x0, x1, x1) | product_3(x1, x1, x1) ....... R1 [B1:L0, B1:L1]
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product_3(x0, x1, x1) | ~product_3(x2, x1, x1) | equalish_2(x2, x1) ....... R2 [R1:L1, B14:L0]
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_1_0(),e_2_0()) ....... U3
% ~product_3(e_1_0(), e_2_0(), e_2_0()) ....... R4 [R3:L1, U3:L0]
% Derivation of unit clause U17:
% ~product_3(x3,x1,x0) | ~product_3(x3,x0,x2) | product_3(x0,x1,x2) ....... B1
% ~product_3(x0, x1, x1) | product_3(x1, x1, x1) ....... R1 [B1:L0, B1:L1]
% ~product_3(x3,x1,x2) | ~product_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product_3(x0, x1, x1) | ~product_3(x2, x1, x1) | equalish_2(x2, x1) ....... R2 [R1:L1, B14:L0]
% ~product_3(x0, x1, x1) | equalish_2(x0, x1) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_2_0(),e_1_0()) ....... U5
% ~product_3(e_2_0(), e_1_0(), e_1_0()) ....... R4 [R3:L1, U5:L0]
% Derivation of unit clause U21:
% ~product_3(x2,x1,x3) | ~product_3(x0,x1,x2) | product_3(x0,x2,x3) ....... B2
% ~product_3(x0, x1, x0) | product_3(x0, x0, x0) ....... R1 [B2:L0, B2:L1]
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product_3(x0, x1, x0) | ~product_3(x0, x2, x0) | equalish_2(x2, x0) ....... R2 [R1:L1, B13:L0]
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_1_0(),e_2_0()) ....... U3
% ~product_3(e_2_0(), e_1_0(), e_2_0()) ....... R4 [R3:L1, U3:L0]
% Derivation of unit clause U23:
% ~product_3(x2,x1,x3) | ~product_3(x0,x1,x2) | product_3(x0,x2,x3) ....... B2
% ~product_3(x0, x1, x0) | product_3(x0, x0, x0) ....... R1 [B2:L0, B2:L1]
% ~product_3(x0,x3,x2) | ~product_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product_3(x0, x1, x0) | ~product_3(x0, x2, x0) | equalish_2(x2, x0) ....... R2 [R1:L1, B13:L0]
% ~product_3(x0, x1, x0) | equalish_2(x1, x0) ....... R3 [R2:L0, R2:L1]
% ~equalish_2(e_2_0(),e_1_0()) ....... U5
% ~product_3(e_1_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U5:L0]
% Derivation of unit clause U27:
% 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(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) ....... R1 [B3:L0, B15:L0]
% group_element_1(e_1_0()) ....... U0
% product_3(e_1_0(), e_1_0(), 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()) ....... R2 [R1:L0, U0:L0]
% ~product_3(e_1_0(),e_1_0(),e_2_0()) ....... U11
% product_3(e_1_0(), e_1_0(), e_1_0()) | product_3(e_1_0(), e_1_0(), e_3_0()) ....... R3 [R2:L1, U11:L0]
% ~product_3(e_1_0(),e_1_0(),e_3_0()) ....... U13
% product_3(e_1_0(), e_1_0(), e_1_0()) ....... R4 [R3:L1, U13:L0]
% Derivation of unit clause U28:
% 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(x0, e_1_0(), e_1_0()) | product_3(x0, e_1_0(), e_2_0()) | product_3(x0, e_1_0(), e_3_0()) ....... R1 [B3:L0, B15:L0]
% group_element_1(e_2_0()) ....... U1
% product_3(e_2_0(), e_1_0(), e_1_0()) | product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) ....... R2 [R1:L0, U1:L0]
% ~product_3(e_2_0(),e_1_0(),e_1_0()) ....... U17
% product_3(e_2_0(), e_1_0(), e_2_0()) | product_3(e_2_0(), e_1_0(), e_3_0()) ....... R3 [R2:L0, U17:L0]
% ~product_3(e_2_0(),e_1_0(),e_2_0()) ....... U21
% product_3(e_2_0(), e_1_0(), e_3_0()) ....... R4 [R3:L0, U21:L0]
% Derivation of unit clause U30:
% 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()) ....... U1
% 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, U1:L0]
% ~product_3(e_1_0(),e_2_0(),e_1_0()) ....... U23
% 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, U23:L0]
% ~product_3(e_1_0(),e_2_0(),e_2_0()) ....... U15
% product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U15:L0]
% Derivation of unit clause U36:
% ~equalish_2(e_1_0(),e_2_0()) ....... B6
% ~product_3(x0,x1,x3) | ~product_3(x0,x1,x2) | equalish_2(x2,x3) ....... B12
% ~product_3(x0, x1, e_2_0()) | ~product_3(x0, x1, e_1_0()) ....... R1 [B6:L0, B12:L2]
% ~product_3(x2,x1,x3) | ~product_3(x0,x2,x3) | product_3(x0,x1,x2) ....... B0
% ~product_3(x0, x1, e_1_0()) | ~product_3(e_2_0(), x1, x2) | ~product_3(x0, e_2_0(), x2) ....... R2 [R1:L0, B0:L2]
% product_3(e_1_0(),e_1_0(),e_1_0()) ....... U27
% ~product_3(e_2_0(), e_1_0(), x0) | ~product_3(e_1_0(), e_2_0(), x0) ....... R3 [R2:L0, U27:L0]
% product_3(e_2_0(),e_1_0(),e_3_0()) ....... U28
% ~product_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U28:L0]
% Derivation of the empty clause:
% ~product_3(e_1_0(),e_2_0(),e_3_0()) ....... U36
% product_3(e_1_0(),e_2_0(),e_3_0()) ....... U30
% [] ....... R1 [U36:L0, U30:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 18600558
% resolvents: 7861670 factors: 10738888
% Number of unit clauses generated: 187973
% % unit clauses generated to total clauses generated: 1.01
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 9 [4] = 28
% Total = 37
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 187973 [2] = 11941170 [3] = 6471289 [4] = 126
% Average size of a generated clause: 3.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] group_element_1 (+)3 (-)0
% [1] equalish_2 (+)0 (-)6
% [2] product_3 (+)9 (-)19
% ------------------
% Total: (+)12 (-)25
% Total number of unit clauses retained: 37
% Number of clauses skipped because of their length: 26459568
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 18600598
% Number of unification failures: 19191521
% Number of unit to unit unification failures: 165
% N literal unification failure due to lookup root_id table: 27761394
% N base clause resolution failure due to lookup table: 896316
% N UC-BCL resolution dropped due to lookup table: 0
% Max entries in substitution set: 24
% N unit clauses dropped because they exceeded max values: 140233
% 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: 34
% Total number of terms of all unit clauses in table: 99
% 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: 0.34
% Number of symbols (columns) in UCFA: 40
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 37792119
% ConstructUnitClause() = 140261
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.11 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 600018
% | |
% --------------------------------------------------------
% Elapsed time: 31 secs
% CPU time: 31.01 secs
%
%------------------------------------------------------------------------------