TSTP Solution File: SET600+3 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 05:10:43 EDT 2022

% Result   : Theorem 0.36s 0.53s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   22 (   6 unt;  11 nHn;  17 RR)
%            Number of literals    :   42 (  19 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ member(X,union(Y,Z))
    | member(X,Y)
    | member(X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

cnf(2,axiom,
    ( member(X,union(Y,Z))
    | ~ member(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

cnf(3,axiom,
    ~ member(X,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

cnf(10,axiom,
    ( ~ empty(X)
    | ~ member(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).

cnf(11,axiom,
    ( empty(X)
    | member('SKOLEMAAAU2'(X),X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).

cnf(12,axiom,
    ( X != Y
    | ~ member(Z,X)
    | member(Z,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

cnf(14,axiom,
    ( X = Y
    | member('SKOLEMAAAU3'(X,Y),X)
    | member('SKOLEMAAAU3'(X,Y),Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

cnf(15,negated_conjecture,
    ( union('SKOLEMAAAU4','SKOLEMAAAU5') != empty_set
    | 'SKOLEMAAAU4' != empty_set
    | 'SKOLEMAAAU5' != empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

cnf(16,negated_conjecture,
    ( union('SKOLEMAAAU4','SKOLEMAAAU5') = empty_set
    | 'SKOLEMAAAU4' = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

cnf(17,negated_conjecture,
    ( union('SKOLEMAAAU4','SKOLEMAAAU5') = empty_set
    | 'SKOLEMAAAU5' = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

cnf(19,plain,
    ( empty(X)
    | member('SKOLEMAAAU2'(X),union(X,Y)) ),
    inference('HYPERRESOLVE',[status(thm)],[2,11]) ).

cnf(25,plain,
    ( 'SKOLEMAAAU5' = empty_set
    | empty(union('SKOLEMAAAU4','SKOLEMAAAU5')) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[12,17,11]),3]) ).

cnf(26,plain,
    ( 'SKOLEMAAAU4' = empty_set
    | empty(union('SKOLEMAAAU4','SKOLEMAAAU5')) ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[12,16,11]),3]) ).

cnf(27,plain,
    ~ member(X,union(empty_set,empty_set)),
    inference('UR-RESOLVE',[status(thm)],[1,3,3]) ).

cnf(29,plain,
    ( empty_set = X
    | member('SKOLEMAAAU3'(empty_set,X),X) ),
    inference('HYPERRESOLVE',[status(thm)],[3,14]) ).

cnf(44,plain,
    union(empty_set,empty_set) = empty_set,
    inference('UR-RESOLVE',[status(thm)],[14,27,3]) ).

cnf(45,plain,
    ( empty('SKOLEMAAAU4')
    | 'SKOLEMAAAU4' = empty_set ),
    inference('HYPERRESOLVE',[status(thm)],[10,19,26]) ).

cnf(48,plain,
    ( empty('SKOLEMAAAU5')
    | 'SKOLEMAAAU5' = empty_set ),
    inference('HYPERRESOLVE',[status(thm)],[10,19,25]) ).

cnf(59,plain,
    'SKOLEMAAAU5' = empty_set,
    inference('HYPERRESOLVE',[status(thm)],[10,29,48]) ).

cnf(60,plain,
    ( union('SKOLEMAAAU4',empty_set) != empty_set
    | 'SKOLEMAAAU4' != empty_set ),
    inference('REWRITE',[status(thm)],[15,59,theory(equality)]) ).

cnf(66,plain,
    'SKOLEMAAAU4' = empty_set,
    inference('HYPERRESOLVE',[status(thm)],[10,29,45]) ).

cnf(67,plain,
    $false,
    inference('REWRITE',[status(thm)],[60,44,66,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 23:28:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46  * 
% 0.20/0.46  * 
% 0.20/0.47  #<PACKAGE "SNARK-USER">
% 0.20/0.47  * 
% 0.20/0.47  SNARK-TPTP-OPTIONS
% 0.20/0.47  * 
% 0.20/0.47  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.47   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.47   (USE-FACTORING :POS)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.47   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.47   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.47   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.47   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.47   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.47   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.47   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.47   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.47   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.47  * 
% 0.20/0.47  "."
% 0.20/0.47  * 
% 0.20/0.47  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T23:28:52
% 0.20/0.47  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n015.cluster.edu at 2022-07-09T23:28:52
% 0.20/0.48  
% 0.20/0.48  ; Recognized commutativity assertion (= (|union| ?X ?Y) (|union| ?Y ?X)).
% 0.36/0.53  ; Declaring union to be commutative.
% 0.36/0.53  
% 0.36/0.53  #||
% 0.36/0.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.53  % SZS output start Refutation
% See solution above
% 0.36/0.53  ||#
% 0.36/0.53  
% 0.36/0.53  ; Summary of computation:
% 0.36/0.53  ;       257 formulas have been input or derived (from 32 formulas).
% 0.36/0.53  ;        67 (26%) were retained.  Of these,
% 0.36/0.53  ;           32 (48%) were simplified or subsumed later,
% 0.36/0.53  ;           35 (52%) are still being kept.
% 0.36/0.53  ; 
% 0.36/0.53  ; Run time in seconds excluding printing time:
% 0.36/0.53  ;     0.002   4%   Read assertion file          (1 call)
% 0.36/0.53  ;     0.001   2%   Assert                       (9 calls)
% 0.36/0.53  ;     0.006  11%   Process new row              (198 calls)
% 0.36/0.53  ;     0.007  13%   Resolution                   (62 calls)
% 0.36/0.53  ;     0.001   2%   Paramodulation               (31 calls)
% 0.36/0.53  ;     0.000   0%   Factoring                    (15 calls)
% 0.36/0.53  ;     0.007  13%   Condensing                   (115 calls)
% 0.36/0.53  ;     0.006  11%   Forward subsumption          (115 calls)
% 0.36/0.53  ;     0.001   2%   Backward subsumption         (56 calls)
% 0.36/0.53  ;     0.000   0%   Clause clause subsumption    (150 calls)
% 0.36/0.53  ;     0.001   2%   Forward simplification       (193 calls)
% 0.36/0.53  ;     0.001   2%   Backward simplification      (67 calls)
% 0.36/0.53  ;     0.000   0%   Ordering                     (330 calls)
% 0.36/0.53  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.36/0.53  ;     0.000   0%   Purity testing               (1 call)
% 0.36/0.53  ;     0.022  40%   Other
% 0.36/0.53  ;     0.055        Total
% 0.36/0.53  ;     0.059        Real time
% 0.36/0.53  ; 
% 0.36/0.53  ; Term-hash-array has 99 terms in all.
% 0.36/0.53  ; Feature-vector-row-index has 27 entries (50 at peak, 56 added, 29 deleted).
% 0.36/0.53  ; Feature-vector-row-index has 62 nodes (160 at peak, 192 added, 130 deleted).
% 0.36/0.53  ;  Retrieved 167 possibly forward subsuming rows in 115 calls.
% 0.36/0.53  ;  Retrieved 27 possibly backward subsumed rows in 56 calls.
% 0.36/0.53  ; Path-index has 69 entries (90 at peak, 102 added, 33 deleted).
% 0.36/0.53  ; Path-index has 85 nodes (112 at peak, 130 added, 45 deleted).
% 0.36/0.53  ; Trie-index has 69 entries (90 at peak, 102 added, 33 deleted).
% 0.36/0.53  ; Trie-index has 124 nodes (168 at peak, 199 added, 75 deleted).
% 0.36/0.53  ; Retrieved 93 generalization terms in 288 calls.
% 0.36/0.53  ; Retrieved 12 instance terms in 10 calls.
% 0.36/0.53  ; Retrieved 1,471 unifiable terms in 225 calls.
% 0.36/0.53  ; 
% 0.36/0.53  ; The agenda of backward simplifiable rows to process has 5 entries:
% 0.36/0.53  ;     5 with value 0
% 0.36/0.53  ; The agenda of rows to process has 18 entries:
% 0.36/0.53  ;     1 with value 11              1 with value 16               4 with value 23
% 0.36/0.53  ;     6 with value 13              2 with value 19               1 with value 29
% 0.36/0.53  ;     1 with value 15              2 with value 20
% 0.36/0.53  ; The agenda of rows to give has 15 entries:
% 0.36/0.53  ;     2 with value (4 7)           1 with value (4 17)           1 with value (4 25)
% 0.36/0.53  ;     1 with value (4 12)          1 with value (4 19)           2 with value (4 26)
% 0.36/0.53  ;     1 with value (4 13)          2 with value (4 21)           2 with value (4 38)
% 0.38/0.53  ;     1 with value (4 16)          1 with value (4 23)
% 0.38/0.53  Evaluation took:
% 0.38/0.53    0.059 seconds of real time
% 0.38/0.53    0.054052 seconds of user run time
% 0.38/0.53    0.004846 seconds of system run time
% 0.38/0.53    0 calls to %EVAL
% 0.38/0.53    0 page faults and
% 0.38/0.53    3,881,336 bytes consed.
% 0.38/0.53  :PROOF-FOUND
% 0.38/0.53  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-09T23:28:52
% 0.38/0.53  :PROOF-FOUND
% 0.38/0.53  * 
%------------------------------------------------------------------------------