TSTP Solution File: GRP123-6.003 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : GRP123-6.003 : TPTP v5.0.0. Released v1.2.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art01.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 20:51:39 EST 2010
% Result : Unsatisfiable 0.30s
% Output : Refutation 0.30s
% 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/SystemOnTPTP19048/GRP/GRP123-6.003+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 = 48] [nf = 0] [nu = 0] [ut = 11]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 316] [nf = 14] [nu = 170] [ut = 48]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 674] [nf = 124] [nu = 352] [ut = 48]
% Looking for a proof at depth = 4 ...
% t = 0 secs [nr = 1848] [nf = 234] [nu = 1086] [ut = 48]
% Looking for a proof at depth = 5 ...
% t = 0 secs [nr = 3250] [nf = 752] [nu = 1820] [ut = 48]
% Looking for a proof at depth = 6 ...
% t = 0 secs [nr = 6404] [nf = 1270] [nu = 3610] [ut = 48]
% Looking for a proof at depth = 7 ...
% t = 0 secs [nr = 9558] [nf = 1788] [nu = 5400] [ut = 48]
% Looking for a proof at depth = 8 ...
% t = 0 secs [nr = 12712] [nf = 2306] [nu = 7190] [ut = 48]
% Looking for a proof at depth = 9 ...
% t = 0 secs [nr = 15866] [nf = 2824] [nu = 8980] [ut = 48]
% Looking for a proof at depth = 10 ...
% t = 0 secs [nr = 19020] [nf = 3342] [nu = 10770] [ut = 48]
% Looking for a proof at depth = 11 ...
% t = 0 secs [nr = 22174] [nf = 3860] [nu = 12560] [ut = 48]
% Looking for a proof at depth = 12 ...
% t = 0 secs [nr = 25328] [nf = 4378] [nu = 14350] [ut = 48]
% Looking for a proof at depth = 13 ...
% t = 0 secs [nr = 28482] [nf = 4896] [nu = 16140] [ut = 48]
% Looking for a proof at depth = 14 ...
% t = 0 secs [nr = 31636] [nf = 5414] [nu = 17930] [ut = 48]
% Looking for a proof at depth = 15 ...
% t = 0 secs [nr = 34790] [nf = 5932] [nu = 19720] [ut = 48]
% Looking for a proof at depth = 16 ...
% t = 0 secs [nr = 37944] [nf = 6450] [nu = 21510] [ut = 48]
% Looking for a proof at depth = 17 ...
% t = 0 secs [nr = 41098] [nf = 6968] [nu = 23300] [ut = 48]
% Looking for a proof at depth = 18 ...
% t = 0 secs [nr = 44252] [nf = 7486] [nu = 25090] [ut = 48]
% Looking for a proof at depth = 19 ...
% t = 0 secs [nr = 47406] [nf = 8004] [nu = 26880] [ut = 48]
% Looking for a proof at depth = 20 ...
% t = 0 secs [nr = 50560] [nf = 8522] [nu = 28670] [ut = 48]
% Looking for a proof at depth = 21 ...
% t = 0 secs [nr = 53714] [nf = 9040] [nu = 30460] [ut = 48]
% Looking for a proof at depth = 22 ...
% t = 0 secs [nr = 56868] [nf = 9558] [nu = 32250] [ut = 48]
% Looking for a proof at depth = 23 ...
% t = 0 secs [nr = 60022] [nf = 10076] [nu = 34040] [ut = 48]
% Looking for a proof at depth = 24 ...
% t = 0 secs [nr = 63176] [nf = 10594] [nu = 35830] [ut = 48]
% Looking for a proof at depth = 25 ...
% t = 0 secs [nr = 66330] [nf = 11112] [nu = 37620] [ut = 48]
% Looking for a proof at depth = 26 ...
% t = 0 secs [nr = 69484] [nf = 11630] [nu = 39410] [ut = 48]
% Looking for a proof at depth = 27 ...
% t = 0 secs [nr = 72638] [nf = 12148] [nu = 41200] [ut = 48]
% Looking for a proof at depth = 28 ...
% t = 0 secs [nr = 75792] [nf = 12666] [nu = 42990] [ut = 48]
% Looking for a proof at depth = 29 ...
% t = 0 secs [nr = 78946] [nf = 13184] [nu = 44780] [ut = 48]
% Looking for a proof at depth = 30 ...
% t = 0 secs [nr = 82100] [nf = 13702] [nu = 46570] [ut = 48]
% Restarting search with different parameters.
% Looking for a proof at depth = 1 ...
% t = 0 secs [nr = 82148] [nf = 13702] [nu = 46570] [ut = 48]
% Looking for a proof at depth = 2 ...
% t = 0 secs [nr = 82446] [nf = 13716] [nu = 46752] [ut = 48]
% Looking for a proof at depth = 3 ...
% t = 0 secs [nr = 82822] [nf = 13826] [nu = 46934] [ut = 48]
% Looking for a proof at depth = 4 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~product1_3(x2,x1,x3) | ~product1_3(x0,x1,x2) | product2_3(x3,x0,x1)
% B1: product1_3(x0,x0,x0)
% B3: group_element_1(e_1_0())
% B4: group_element_1(e_2_0())
% B6: ~equalish_2(e_1_0(),e_2_0())
% B13: ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3)
% B14: ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3)
% B15: ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3)
% B18: ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0())
% Unit Clauses:
% --------------
% U1: < d0 v3 dv1 f0 c0 t3 td1 b > product2_3(x0,x0,x0)
% U3: < d0 v0 dv0 f0 c1 t1 td1 b > group_element_1(e_2_0())
% U4: < 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())
% U10: < d0 v0 dv0 f0 c2 t2 td1 b > ~equalish_2(e_3_0(),e_2_0())
% U20: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_1_0())
% U21: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_3_0())
% U24: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_2_0())
% U29: < d2 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_3_0(),e_2_0(),e_2_0())
% U51: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_1_0(),e_2_0(),e_3_0())
% U59: < d4 v0 dv0 f0 c3 t3 td1 > product1_3(e_3_0(),e_2_0(),e_1_0())
% U66: < d4 v0 dv0 f0 c3 t3 td1 > ~product1_3(e_1_0(),e_2_0(),e_3_0())
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% product2_3(x0,x0,x0) ....... U1
% Derivation of unit clause U3:
% group_element_1(e_2_0()) ....... U3
% Derivation of unit clause U4:
% group_element_1(e_3_0()) ....... U4
% 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 U10:
% ~equalish_2(e_3_0(),e_2_0()) ....... U10
% Derivation of unit clause U20:
% product1_3(x0,x0,x0) ....... B1
% ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B13:L0]
% ~equalish_2(e_2_0(),e_1_0()) ....... U7
% ~product1_3(e_1_0(), e_2_0(), e_1_0()) ....... R2 [R1:L1, U7:L0]
% Derivation of unit clause U21:
% product1_3(x0,x0,x0) ....... B1
% ~product1_3(x0,x3,x2) | ~product1_3(x0,x1,x2) | equalish_2(x1,x3) ....... B13
% ~product1_3(x0, x1, x0) | equalish_2(x1, x0) ....... R1 [B1:L0, B13:L0]
% ~equalish_2(e_2_0(),e_3_0()) ....... U8
% ~product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L1, U8:L0]
% Derivation of unit clause U24:
% product1_3(x0,x0,x0) ....... B1
% ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B14:L0]
% ~equalish_2(e_1_0(),e_2_0()) ....... U5
% ~product1_3(e_1_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U5:L0]
% Derivation of unit clause U29:
% product1_3(x0,x0,x0) ....... B1
% ~product1_3(x3,x1,x2) | ~product1_3(x0,x1,x2) | equalish_2(x0,x3) ....... B14
% ~product1_3(x0, x1, x1) | equalish_2(x0, x1) ....... R1 [B1:L0, B14:L0]
% ~equalish_2(e_3_0(),e_2_0()) ....... U10
% ~product1_3(e_3_0(), e_2_0(), e_2_0()) ....... R2 [R1:L1, U10:L0]
% Derivation of unit clause U51:
% group_element_1(e_1_0()) ....... B3
% ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0()) ....... B18
% ~group_element_1(x0) | product1_3(e_1_0(), x0, e_1_0()) | product1_3(e_1_0(), x0, e_2_0()) | product1_3(e_1_0(), x0, e_3_0()) ....... R1 [B3:L0, B18:L1]
% group_element_1(e_2_0()) ....... U3
% product1_3(e_1_0(), e_2_0(), e_1_0()) | product1_3(e_1_0(), e_2_0(), e_2_0()) | product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U3:L0]
% ~product1_3(e_1_0(),e_2_0(),e_1_0()) ....... U20
% product1_3(e_1_0(), e_2_0(), e_2_0()) | product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R3 [R2:L0, U20:L0]
% ~product1_3(e_1_0(),e_2_0(),e_2_0()) ....... U24
% product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U24:L0]
% Derivation of unit clause U59:
% group_element_1(e_2_0()) ....... B4
% ~group_element_1(x1) | ~group_element_1(x0) | product1_3(x0,x1,e_1_0()) | product1_3(x0,x1,e_2_0()) | product1_3(x0,x1,e_3_0()) ....... B18
% ~group_element_1(x0) | product1_3(x0, e_2_0(), e_1_0()) | product1_3(x0, e_2_0(), e_2_0()) | product1_3(x0, e_2_0(), e_3_0()) ....... R1 [B4:L0, B18:L0]
% group_element_1(e_3_0()) ....... U4
% product1_3(e_3_0(), e_2_0(), e_1_0()) | product1_3(e_3_0(), e_2_0(), e_2_0()) | product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R2 [R1:L0, U4:L0]
% ~product1_3(e_3_0(),e_2_0(),e_2_0()) ....... U29
% product1_3(e_3_0(), e_2_0(), e_1_0()) | product1_3(e_3_0(), e_2_0(), e_3_0()) ....... R3 [R2:L1, U29:L0]
% ~product1_3(e_3_0(),e_2_0(),e_3_0()) ....... U21
% product1_3(e_3_0(), e_2_0(), e_1_0()) ....... R4 [R3:L1, U21:L0]
% Derivation of unit clause U66:
% ~equalish_2(e_1_0(),e_2_0()) ....... B6
% ~product2_3(x0,x1,x3) | ~product2_3(x0,x1,x2) | equalish_2(x2,x3) ....... B15
% ~product2_3(x0, x1, e_2_0()) | ~product2_3(x0, x1, e_1_0()) ....... R1 [B6:L0, B15:L2]
% ~product1_3(x2,x1,x3) | ~product1_3(x0,x1,x2) | product2_3(x3,x0,x1) ....... B0
% ~product2_3(x0, x1, e_1_0()) | ~product1_3(x2, e_2_0(), x0) | ~product1_3(x1, e_2_0(), x2) ....... R2 [R1:L0, B0:L2]
% product2_3(x0,x0,x0) ....... U1
% ~product1_3(x0, e_2_0(), e_1_0()) | ~product1_3(e_1_0(), e_2_0(), x0) ....... R3 [R2:L0, U1:L0]
% product1_3(e_3_0(),e_2_0(),e_1_0()) ....... U59
% ~product1_3(e_1_0(), e_2_0(), e_3_0()) ....... R4 [R3:L0, U59:L0]
% Derivation of the empty clause:
% ~product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U66
% product1_3(e_1_0(),e_2_0(),e_3_0()) ....... U51
% [] ....... R1 [U66:L0, U51:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 98575
% resolvents: 84733 factors: 13842
% Number of unit clauses generated: 47997
% % unit clauses generated to total clauses generated: 48.69
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 11 [2] = 37 [4] = 19
% Total = 67
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 47997 [2] = 42693 [3] = 7849 [4] = 36
% Average size of a generated clause: 2.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] group_element_1 (+)3 (-)0
% [1] equalish_2 (+)1 (-)6
% [2] product1_3 (+)10 (-)19
% [3] product2_3 (+)10 (-)18
% ------------------
% Total: (+)24 (-)43
% Total number of unit clauses retained: 67
% Number of clauses skipped because of their length: 17388
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 0
% Number of successful unifications: 98595
% Number of unification failures: 81131
% Number of unit to unit unification failures: 370
% N literal unification failure due to lookup root_id table: 593160
% N base clause resolution failure due to lookup table: 265894
% 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: 2837
% 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: 66
% Total number of terms of all unit clauses in table: 188
% 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: 0.35
% Number of symbols (columns) in UCFA: 41
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 179726
% ConstructUnitClause() = 2893
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.00 secs
% --------------------------------------------------------
% | |
% Inferences per sec: inf
% | |
% --------------------------------------------------------
% Elapsed time: 0 secs
% CPU time: 0.29 secs
%
%------------------------------------------------------------------------------