TSTP Solution File: SET984+1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n005.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 05:13:50 EDT 2022

% Result   : Theorem 0.47s 0.71s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   10
% Syntax   : Number of clauses     :   19 (  13 unt;   2 nHn;  15 RR)
%            Number of literals    :   29 (  21 equ;  11 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   20 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(7,axiom,
    ( cartesian_product2(X,Y) = empty_set
    | X != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

cnf(8,axiom,
    ( cartesian_product2(X,Y) = empty_set
    | Y != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

cnf(9,axiom,
    cartesian_product2(set_intersection2(X,Y),set_intersection2(Z,U)) = set_intersection2(cartesian_product2(X,Z),cartesian_product2(Y,U)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).

cnf(10,axiom,
    ( cartesian_product2(X,Y) != cartesian_product2(Z,U)
    | X = empty_set
    | Y = empty_set
    | X = Z ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

cnf(11,axiom,
    ( cartesian_product2(X,Y) != cartesian_product2(Z,U)
    | X = empty_set
    | Y = empty_set
    | Y = U ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

cnf(12,negated_conjecture,
    subset(cartesian_product2('SKOLEMAAAW3','SKOLEMAAAW4'),cartesian_product2('SKOLEMAAAW5','SKOLEMAAAW6')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

cnf(13,negated_conjecture,
    cartesian_product2('SKOLEMAAAW3','SKOLEMAAAW4') != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

cnf(14,negated_conjecture,
    ( ~ subset('SKOLEMAAAW3','SKOLEMAAAW5')
    | ~ subset('SKOLEMAAAW4','SKOLEMAAAW6') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

cnf(15,axiom,
    subset(set_intersection2(X,Y),X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

cnf(16,axiom,
    ( ~ subset(X,Y)
    | set_intersection2(X,Y) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

cnf(17,plain,
    'SKOLEMAAAW3' != empty_set,
    inference('UR-RESOLVE',[status(thm)],[7,13]) ).

cnf(19,plain,
    'SKOLEMAAAW4' != empty_set,
    inference('UR-RESOLVE',[status(thm)],[8,13]) ).

cnf(22,plain,
    cartesian_product2(set_intersection2('SKOLEMAAAW3','SKOLEMAAAW5'),set_intersection2('SKOLEMAAAW4','SKOLEMAAAW6')) = cartesian_product2('SKOLEMAAAW3','SKOLEMAAAW4'),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[16,12]),9,theory(equality)]) ).

cnf(554,plain,
    'SKOLEMAAAW4' = set_intersection2('SKOLEMAAAW4','SKOLEMAAAW6'),
    inference('UR-RESOLVE',[status(thm)],[11,22,17,19]) ).

cnf(555,plain,
    cartesian_product2(set_intersection2('SKOLEMAAAW3','SKOLEMAAAW5'),'SKOLEMAAAW4') = cartesian_product2('SKOLEMAAAW3','SKOLEMAAAW4'),
    inference('REWRITE',[status(thm)],[22,554,theory(equality)]) ).

cnf(556,plain,
    subset('SKOLEMAAAW4','SKOLEMAAAW6'),
    inference('PARAMODULATE',[status(thm)],[15,554,theory(equality)]) ).

cnf(557,plain,
    ~ subset('SKOLEMAAAW3','SKOLEMAAAW5'),
    inference('REWRITE',[status(thm)],[14,556]) ).

cnf(558,plain,
    'SKOLEMAAAW3' = set_intersection2('SKOLEMAAAW3','SKOLEMAAAW5'),
    inference('UR-RESOLVE',[status(thm)],[10,555,17,19]) ).

cnf(559,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,558,theory(equality)]),557]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET984+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 06:36:22 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48  * 
% 0.20/0.48  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T06:36:22
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n005.cluster.edu at 2022-07-10T06:36:22
% 0.20/0.50  
% 0.20/0.50  ; Recognized commutativity assertion (= (|set_intersection2| ?X ?Y) (|set_intersection2| ?Y ?X)).
% 0.47/0.71  ; Declaring set_intersection2 to be commutative.
% 0.47/0.71  
% 0.47/0.71  #||
% 0.47/0.71  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.71  % SZS output start Refutation
% See solution above
% 0.47/0.72  ||#
% 0.47/0.72  
% 0.47/0.72  ; Summary of computation:
% 0.47/0.72  ;      3561 formulas have been input or derived (from 48 formulas).
% 0.47/0.72  ;       559 (16%) were retained.  Of these,
% 0.47/0.72  ;            3 ( 1%) were simplified or subsumed later,
% 0.47/0.72  ;          556 (99%) are still being kept.
% 0.47/0.72  ; 
% 0.47/0.72  ; Run time in seconds excluding printing time:
% 0.47/0.72  ;     0.003   1%   Read assertion file          (1 call)
% 0.47/0.72  ;     0.000   0%   Assert                       (12 calls)
% 0.47/0.72  ;     0.034  15%   Process new row              (2,950 calls)
% 0.47/0.72  ;     0.084  37%   Resolution                   (94 calls)
% 0.47/0.72  ;     0.005   2%   Paramodulation               (47 calls)
% 0.47/0.72  ;     0.000   0%   Condensing                   (11 calls)
% 0.47/0.72  ;     0.001   0%   Forward subsumption          (11 calls)
% 0.47/0.72  ;     0.000   0%   Backward subsumption         (7 calls)
% 0.47/0.72  ;     0.001   0%   Clause clause subsumption    (8 calls)
% 0.47/0.72  ;     0.048  21%   Forward simplification       (2,925 calls)
% 0.47/0.72  ;     0.010   4%   Backward simplification      (559 calls)
% 0.47/0.72  ;     0.001   0%   Ordering                     (201 calls)
% 0.47/0.72  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.47/0.72  ;     0.000   0%   Purity testing               (1 call)
% 0.47/0.72  ;     0.039  17%   Other
% 0.47/0.72  ;     0.226        Total
% 0.47/0.72  ;     0.238        Real time
% 0.47/0.72  ; 
% 0.47/0.72  ; Term-hash-array has 1,113 terms in all.
% 0.47/0.72  ; Feature-vector-row-index has 6 entries (7 at peak, 7 added, 1 deleted).
% 0.47/0.72  ; Feature-vector-row-index has 21 nodes (27 at peak, 27 added, 6 deleted).
% 0.47/0.72  ;  Retrieved 6 possibly forward subsuming rows in 11 calls.
% 0.47/0.72  ;  Retrieved 2 possibly backward subsumed rows in 7 calls.
% 0.47/0.72  ; Path-index has 1,116 entries (1,118 at peak, 1,122 added, 6 deleted).
% 0.47/0.72  ; Path-index has 192 nodes (198 at peak, 208 added, 16 deleted).
% 0.47/0.72  ; Trie-index has 1,116 entries (1,118 at peak, 1,122 added, 6 deleted).
% 0.47/0.72  ; Trie-index has 2,645 nodes (2,655 at peak, 2,671 added, 26 deleted).
% 0.47/0.72  ; Retrieved 3,444 generalization terms in 12,902 calls.
% 0.47/0.72  ; Retrieved 553 instance terms in 553 calls.
% 0.47/0.72  ; Retrieved 155,201 unifiable terms in 3,832 calls.
% 0.47/0.72  ; 
% 0.47/0.72  ; The agenda of rows to process has 2 entries:
% 0.47/0.72  ;     2 with value 10
% 0.47/0.72  ; The agenda of rows to give has 511 entries:
% 0.47/0.72  ;    16 with value (4 15)         34 with value (4 18)         240 with value (4 21)
% 0.47/0.72  ;    16 with value (4 16)         98 with value (4 19)           8 with value (4 22)
% 0.47/0.72  ;    52 with value (4 17)         22 with value (4 20)          25 with value (4 23)
% 0.47/0.72  Evaluation took:
% 0.47/0.72    0.238 seconds of real time
% 0.47/0.72    0.213723 seconds of user run time
% 0.47/0.72    0.024838 seconds of system run time
% 0.47/0.72    [Run times include 0.01 seconds GC run time.]
% 0.47/0.72    0 calls to %EVAL
% 0.47/0.72    0 page faults and
% 0.47/0.72    13,167,448 bytes consed.
% 0.47/0.72  :PROOF-FOUND
% 0.47/0.72  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-10T06:36:22
% 0.47/0.72  :PROOF-FOUND
% 0.47/0.72  * 
%------------------------------------------------------------------------------