TSTP Solution File: SET011-1 by CARINE---0.734
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%------------------------------------------------------------------------------
% File : CARINE---0.734
% Problem : SET011-1 : TPTP v5.0.0. Released v1.0.0.
% Transfm : add_equality
% Format : carine
% Command : carine %s t=%d xo=off uct=32000
% Computer : art02.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 04:47:08 EST 2010
% Result : Unsatisfiable 3.04s
% Output : Refutation 3.04s
% 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/SystemOnTPTP1722/SET/SET011-1+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 = 7] [nf = 0] [nu = 0] [ut = 3]
% Looking for a proof at depth = 2 ...
% t = 1 secs [nr = 74] [nf = 17] [nu = 3] [ut = 5]
% Looking for a proof at depth = 3 ...
% t = 1 secs [nr = 585] [nf = 137] [nu = 32] [ut = 5]
% Looking for a proof at depth = 4 ...
% t = 1 secs [nr = 3427] [nf = 550] [nu = 315] [ut = 11]
% Looking for a proof at depth = 5 ...
% t = 1 secs [nr = 18381] [nf = 3089] [nu = 1453] [ut = 11]
% Looking for a proof at depth = 6 ...
% t = 3 secs [nr = 775257] [nf = 80729] [nu = 124010] [ut = 144]
% Looking for a proof at depth = 7 ...
% +================================================+
% | |
% | Congratulations!!! ........ A proof was found. |
% | |
% +================================================+
% Base Clauses and Unit Clauses used in proof:
% ============================================
% Base Clauses:
% -------------
% B0: ~intersection_3(a_0(),b_0(),aD_aDb_0())
% B1: difference_3(a_0(),b_0(),aDb_0())
% B2: difference_3(a_0(),aDb_0(),aD_aDb_0())
% B5: member_2(member_of_1_not_of_2_2(x0,x1),x0) | subset_2(x0,x1)
% B6: ~member_2(member_of_1_not_of_2_2(x0,x1),x1) | subset_2(x0,x1)
% B12: member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x0) | intersection_3(x0,x1,x2)
% B13: member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x1) | intersection_3(x0,x1,x2)
% B16: ~subset_2(x1,x0) | ~subset_2(x0,x1) | equal_sets_2(x1,x0)
% B18: ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2)
% B19: ~member_2(h_3(x0,x1,x2),x0) | ~member_2(h_3(x0,x1,x2),x1) | ~member_2(h_3(x0,x1,x2),x2) | intersection_3(x0,x1,x2)
% Unit Clauses:
% --------------
% U1: < d0 v0 dv0 f0 c3 t3 td1 b > difference_3(a_0(),b_0(),aDb_0())
% U2: < d0 v0 dv0 f0 c3 t3 td1 b > difference_3(a_0(),aDb_0(),aD_aDb_0())
% U3: < d2 v2 dv1 f0 c0 t2 td1 > subset_2(x0,x0)
% U4: < d2 v2 dv1 f0 c0 t2 td1 > equal_sets_2(x0,x0)
% U5: < d4 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0())
% U12: < d6 v0 dv0 f1 c4 t5 td2 > ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0())
% U34: < d6 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),b_0())
% U70: < d6 v0 dv0 f1 c4 t5 td2 > member_2(h_3(a_0(),b_0(),aD_aDb_0()),aD_aDb_0())
% U193: < d7 v0 dv0 f0 c2 t2 td1 > ~subset_2(b_0(),b_0())
% --------------- Start of Proof ---------------
% Derivation of unit clause U1:
% difference_3(a_0(),b_0(),aDb_0()) ....... U1
% Derivation of unit clause U2:
% difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2
% Derivation of unit clause U3:
% member_2(member_of_1_not_of_2_2(x0,x1),x0) | subset_2(x0,x1) ....... B5
% ~member_2(member_of_1_not_of_2_2(x0,x1),x1) | subset_2(x0,x1) ....... B6
% subset_2(x0, x0) | subset_2(x0, x0) ....... R1 [B5:L0, B6:L0]
% subset_2(x0, x0) ....... R2 [R1:L0, R1:L1]
% Derivation of unit clause U4:
% ~subset_2(x1,x0) | ~subset_2(x0,x1) | equal_sets_2(x1,x0) ....... B16
% ~subset_2(x0, x0) | equal_sets_2(x0, x0) ....... R1 [B16:L0, B16:L1]
% subset_2(x0,x0) ....... U3
% equal_sets_2(x0, x0) ....... R2 [R1:L0, U3:L0]
% Derivation of unit clause U5:
% ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0
% member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x0) | intersection_3(x0,x1,x2) ....... B12
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R1 [B0:L0, B12:L2]
% ~member_2(x3,x2) | ~difference_3(x0,x1,x2) | member_2(x3,x0) ....... B8
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) | ~difference_3(x0, x1, aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R2 [R1:L0, B8:L0]
% ~difference_3(a_0(), x0, aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R3 [R2:L0, R2:L2]
% difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) ....... R4 [R3:L0, U2:L0]
% Derivation of unit clause U12:
% ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0
% member_2(h_3(x0,x1,x2),x2) | member_2(h_3(x0,x1,x2),x1) | intersection_3(x0,x1,x2) ....... B13
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R1 [B0:L0, B13:L2]
% ~member_2(x0,x2) | ~member_2(x0,x1) | ~difference_3(x3,x1,x2) ....... B7
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~difference_3(x1, x0, aD_aDb_0()) ....... R2 [R1:L0, B7:L0]
% difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... U2
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R3 [R2:L2, U2:L0]
% ~member_2(x0,x2) | ~member_2(x0,x1) | ~difference_3(x3,x1,x2) ....... B7
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~difference_3(x1, b_0(), x0) ....... R4 [R3:L0, B7:L1]
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~difference_3(x0, b_0(), aDb_0()) ....... R5 [R4:L0, R4:L1]
% difference_3(a_0(),b_0(),aDb_0()) ....... U1
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R6 [R5:L1, U1:L0]
% Derivation of unit clause U34:
% difference_3(a_0(),b_0(),aDb_0()) ....... B1
% ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2) ....... B18
% ~member_2(x0, a_0()) | member_2(x0, aDb_0()) | member_2(x0, b_0()) ....... R1 [B1:L0, B18:L1]
% member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R2 [R1:L0, U5:L0]
% ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R3 [R2:L0, B11:L0]
% ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0()) ....... U12
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(aDb_0(), aDb_0()) ....... R4 [R3:L2, U12:L0]
% ~equal_sets_2(x0,x1) | subset_2(x0,x1) ....... B3
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~equal_sets_2(aDb_0(), aDb_0()) ....... R5 [R4:L1, B3:L1]
% equal_sets_2(x0,x0) ....... U4
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) ....... R6 [R5:L1, U4:L0]
% Derivation of unit clause U70:
% difference_3(a_0(),aDb_0(),aD_aDb_0()) ....... B2
% ~member_2(x0,x1) | ~difference_3(x1,x2,x3) | member_2(x0,x3) | member_2(x0,x2) ....... B18
% ~member_2(x0, a_0()) | member_2(x0, aD_aDb_0()) | member_2(x0, aDb_0()) ....... R1 [B2:L0, B18:L1]
% member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) ....... R2 [R1:L0, U5:L0]
% ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aDb_0()) | ~subset_2(aD_aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R3 [R2:L0, B11:L0]
% ~member_2(h_3(a_0(),b_0(),aD_aDb_0()),aDb_0()) ....... U12
% ~subset_2(aD_aDb_0(), x0) | member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) ....... R4 [R3:L0, U12:L0]
% ~equal_sets_2(x0,x1) | subset_2(x0,x1) ....... B3
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~equal_sets_2(aD_aDb_0(), x0) ....... R5 [R4:L0, B3:L1]
% equal_sets_2(x0,x0) ....... U4
% member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R6 [R5:L1, U4:L0]
% Derivation of unit clause U193:
% ~intersection_3(a_0(),b_0(),aD_aDb_0()) ....... B0
% ~member_2(h_3(x0,x1,x2),x0) | ~member_2(h_3(x0,x1,x2),x1) | ~member_2(h_3(x0,x1,x2),x2) | intersection_3(x0,x1,x2) ....... B19
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), a_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R1 [B0:L0, B19:L3]
% member_2(h_3(a_0(),b_0(),aD_aDb_0()),a_0()) ....... U5
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) ....... R2 [R1:L0, U5:L0]
% ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), aD_aDb_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~subset_2(x0, b_0()) ....... R3 [R2:L0, B11:L2]
% member_2(h_3(a_0(),b_0(),aD_aDb_0()),aD_aDb_0()) ....... U70
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x0) | ~subset_2(x0, b_0()) ....... R4 [R3:L0, U70:L0]
% ~member_2(x0,x1) | ~subset_2(x1,x2) | member_2(x0,x2) ....... B11
% ~subset_2(x0, b_0()) | ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), x1) | ~subset_2(x1, x0) ....... R5 [R4:L0, B11:L2]
% ~member_2(h_3(a_0(), b_0(), aD_aDb_0()), b_0()) | ~subset_2(b_0(), b_0()) ....... R6 [R5:L0, R5:L2]
% member_2(h_3(a_0(),b_0(),aD_aDb_0()),b_0()) ....... U34
% ~subset_2(b_0(), b_0()) ....... R7 [R6:L0, U34:L0]
% Derivation of the empty clause:
% ~subset_2(b_0(),b_0()) ....... U193
% subset_2(x0,x0) ....... U3
% [] ....... R1 [U193:L0, U3:L0]
% --------------- End of Proof ---------------
% PROOF FOUND!
% ---------------------------------------------
% | Statistics |
% ---------------------------------------------
% Profile 3: Performance Statistics:
% ==================================
% Total number of generated clauses: 876844
% resolvents: 792655 factors: 84189
% Number of unit clauses generated: 124538
% % unit clauses generated to total clauses generated: 14.20
% Number of unit clauses constructed and retained at depth [x]:
% =============================================================
% [0] = 3 [2] = 2 [4] = 6 [6] = 133 [7] = 50
% Total = 194
% Number of generated clauses having [x] literals:
% ------------------------------------------------
% [1] = 124538 [2] = 393786 [3] = 358520
% Average size of a generated clause: 3.0
% Number of unit clauses per predicate list:
% ==========================================
% [0] equal_sets_2 (+)1 (-)6
% [1] member_2 (+)67 (-)21
% [2] subset_2 (+)4 (-)6
% [3] difference_3 (+)2 (-)40
% [4] intersection_3 (+)0 (-)47
% ------------------
% Total: (+)74 (-)120
% Total number of unit clauses retained: 194
% Number of clauses skipped because of their length: 2032957
% N base clauses skippped in resolve-with-all-base-clauses
% because of the shortest resolvents table: 17319
% Number of successful unifications: 876877
% Number of unification failures: 6650478
% Number of unit to unit unification failures: 1513
% N literal unification failure due to lookup root_id table: 3547225
% N base clause resolution failure due to lookup table: 1359533
% N UC-BCL resolution dropped due to lookup table: 10856
% Max entries in substitution set: 15
% N unit clauses dropped because they exceeded max values: 101628
% 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: 5
% Max term depth in a unit clause: 2
% Number of states in UCFA table: 230
% Total number of terms of all unit clauses in table: 732
% 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: 0.31
% Number of symbols (columns) in UCFA: 46
% Profile 2: Number of calls to:
% ==============================
% PTUnify() = 7527355
% ConstructUnitClause() = 101819
% Profile 1: Time spent in:
% =========================
% ConstructUnitClause() : 0.10 secs
% --------------------------------------------------------
% | |
% Inferences per sec: 292281
% | |
% --------------------------------------------------------
% Elapsed time: 3 secs
% CPU time: 3.04 secs
%
%------------------------------------------------------------------------------