TSTP Solution File: SET116-7 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n006.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 05:07:34 EDT 2022

% Result   : Unsatisfiable 0.71s 0.90s
% Output   : Refutation 0.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  11 unt;   4 nHn;   6 RR)
%            Number of literals    :   19 (  18 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :   11 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   1 con; 0-2 aty)
%            Number of variables   :   14 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
    unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

cnf(union,axiom,
    complement(intersection(complement(X),complement(Y))) = union(X,Y),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).

cnf(unordered_pairs_and_singletons,axiom,
    unordered_pair(X,Y) = union(singleton(X),singleton(Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).

cnf(148,plain,
    unordered_pair(X,Y) = complement(intersection(complement(singleton(X)),complement(singleton(Y)))),
    inference('REWRITE',[status(thm)],[unordered_pairs_and_singletons,union,theory(equality)]) ).

cnf(existence_of_1st_and_2nd_4,axiom,
    ( ordered_pair(first(X),second(X)) = X
    | first(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).

cnf(existence_of_1st_and_2nd_5,axiom,
    ( ordered_pair(first(X),second(X)) = X
    | second(X) = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).

cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets4_1,negated_conjecture,
    ordered_pair(first(x),second(x)) != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets4_1) ).

cnf(prove_unique_2nd_in_pair_of_non_sets,negated_conjecture,
    second(x) != x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).

cnf(172,plain,
    complement(intersection(complement(singleton(singleton(X))),complement(singleton(complement(intersection(complement(singleton(X)),complement(singleton(singleton(Y))))))))) = ordered_pair(X,Y),
    inference('REWRITE',[status(thm)],[ordered_pair,148,theory(equality)]) ).

cnf(176,plain,
    ( complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))) = X
    | first(X) = X ),
    inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_4,172,theory(equality)]) ).

cnf(177,plain,
    ( complement(intersection(complement(singleton(singleton(first(X)))),complement(singleton(complement(intersection(complement(singleton(first(X))),complement(singleton(singleton(second(X)))))))))) = X
    | second(X) = X ),
    inference('REWRITE',[status(thm)],[existence_of_1st_and_2nd_5,172,theory(equality)]) ).

cnf(178,plain,
    complement(intersection(complement(singleton(singleton(first(x)))),complement(singleton(complement(intersection(complement(singleton(first(x))),complement(singleton(singleton(second(x)))))))))) != x,
    inference('REWRITE',[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_non_sets4_1,172,theory(equality)]) ).

cnf(791,plain,
    first(x) = x,
    inference('HYPERRESOLVE',[status(thm)],[178,176]) ).

cnf(792,plain,
    complement(intersection(complement(singleton(singleton(x))),complement(singleton(complement(intersection(complement(singleton(x)),complement(singleton(singleton(second(x)))))))))) != x,
    inference('REWRITE',[status(thm)],[178,791,theory(equality)]) ).

cnf(841,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[177,prove_unique_2nd_in_pair_of_non_sets]),792,791,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET116-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.13  % Command  : run-snark %s %d
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jul 10 18:35:21 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.46  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47  * 
% 0.21/0.47  * 
% 0.21/0.48  #<PACKAGE "SNARK-USER">
% 0.21/0.48  * 
% 0.21/0.48  SNARK-TPTP-OPTIONS
% 0.21/0.48  * 
% 0.21/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.48   (USE-FACTORING :POS)
% 0.21/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.48  * 
% 0.21/0.48  "."
% 0.21/0.48  * 
% 0.21/0.48  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T18:35:21
% 0.21/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-07-10T18:35:21
% 0.21/0.52  
% 0.21/0.53  ; Recognized commutativity assertion (= (|unordered_pair| ?X ?Y) (|unordered_pair| ?Y ?X)).
% 0.71/0.90  ; Declaring unordered_pair to be commutative.
% 0.71/0.90  
% 0.71/0.90  #||
% 0.71/0.90  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.71/0.90  % SZS output start Refutation
% See solution above
% 0.71/0.90  ||#
% 0.71/0.90  
% 0.71/0.90  ; Summary of computation:
% 0.71/0.90  ;      1886 formulas have been input or derived (from 125 formulas).
% 0.71/0.90  ;       841 (45%) were retained.  Of these,
% 0.71/0.90  ;           84 (10%) were simplified or subsumed later,
% 0.71/0.90  ;          757 (90%) are still being kept.
% 0.71/0.90  ; 
% 0.71/0.90  ; Run time in seconds excluding printing time:
% 0.71/0.90  ;     0.029   7%   Read assertion file          (1 call)
% 0.71/0.90  ;     0.004   1%   Assert                       (161 calls)
% 0.71/0.90  ;     0.092  22%   Process new row              (1,708 calls)
% 0.71/0.90  ;     0.030   7%   Resolution                   (248 calls)
% 0.71/0.90  ;     0.022   5%   Paramodulation               (124 calls)
% 0.71/0.90  ;     0.000   0%   Factoring                    (16 calls)
% 0.71/0.90  ;     0.014   3%   Condensing                   (850 calls)
% 0.71/0.90  ;     0.100  24%   Forward subsumption          (850 calls)
% 0.71/0.90  ;     0.022   5%   Backward subsumption         (641 calls)
% 0.71/0.90  ;     0.007   2%   Clause clause subsumption    (2,708 calls)
% 0.71/0.90  ;     0.047  11%   Forward simplification       (1,705 calls)
% 0.71/0.90  ;     0.007   2%   Backward simplification      (824 calls)
% 0.71/0.90  ;     0.010   2%   Ordering                     (2,440 calls)
% 0.71/0.90  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.71/0.90  ;     0.000   0%   Purity testing               (1 call)
% 0.71/0.90  ;     0.032   8%   Other
% 0.71/0.90  ;     0.416        Total
% 0.71/0.90  ;     0.419        Real time
% 0.71/0.90  ; 
% 0.71/0.90  ; Term-hash-array has 2,063 terms in all.
% 0.71/0.90  ; Feature-vector-row-index has 597 entries (597 at peak, 641 added, 44 deleted).
% 0.71/0.90  ; Feature-vector-row-index has 4,560 nodes (4,560 at peak, 4,812 added, 252 deleted).
% 0.71/0.90  ;  Retrieved 4,328 possibly forward subsuming rows in 850 calls.
% 0.71/0.90  ;  Retrieved 318 possibly backward subsumed rows in 641 calls.
% 0.71/0.90  ; Path-index has 1,961 entries (1,961 at peak, 2,126 added, 165 deleted).
% 0.71/0.90  ; Path-index has 7,811 nodes (7,811 at peak, 8,065 added, 254 deleted).
% 0.71/0.90  ; Trie-index has 1,961 entries (1,961 at peak, 2,126 added, 165 deleted).
% 0.71/0.90  ; Trie-index has 9,950 nodes (9,950 at peak, 10,660 added, 710 deleted).
% 0.71/0.90  ; Retrieved 4,420 generalization terms in 10,545 calls.
% 0.71/0.90  ; Retrieved 325 instance terms in 182 calls.
% 0.71/0.90  ; Retrieved 26,357 unifiable terms in 1,499 calls.
% 0.71/0.90  ; 
% 0.71/0.90  ; The agenda of rows to process has 22 entries:
% 0.71/0.90  ;     1 with value 39              1 with value 49               1 with value 64
% 0.71/0.90  ;     2 with value 40              1 with value 53               1 with value 66
% 0.71/0.90  ;     1 with value 42              1 with value 57               2 with value 71
% 0.71/0.90  ;     3 with value 43              3 with value 59               1 with value 104
% 0.71/0.90  ;     1 with value 45              2 with value 62               1 with value 127
% 0.71/0.90  ; The agenda of input rows to give has 27 entries:
% 0.71/0.90  ;     2 with value 39              2 with value 53               1 with value 74
% 0.71/0.90  ;     1 with value 40              1 with value 56               2 with value 94
% 0.71/0.90  ;     2 with value 41              1 with value 57               1 with value 123
% 0.71/0.90  ;     1 with value 43              2 with value 62               2 with value 139
% 0.71/0.90  ;     4 with value 46              1 with value 64               2 with value 212
% 0.71/0.90  ;     1 with value 48              1 with value 66
% 0.71/0.90  ; The agenda of rows to give has 607 entries:
% 0.71/0.90  ;     2 with value (4 4)           5 with value (4 29)           4 with value (4 54)
% 0.71/0.90  ;     2 with value (4 5)          13 with value (4 30)           2 with value (4 55)
% 0.71/0.90  ;    16 with value (4 7)          19 with value (4 31)           5 with value (4 57)
% 0.71/0.90  ;    11 with value (4 8)           8 with value (4 32)           4 with value (4 58)
% 0.71/0.90  ;    11 with value (4 9)          11 with value (4 33)           7 with value (4 59)
% 0.71/0.90  ;     8 with value (4 10)         10 with value (4 34)           1 with value (4 60)
% 0.71/0.90  ;    10 with value (4 11)         10 with value (4 35)           4 with value (4 62)
% 0.71/0.90  ;     9 with value (4 12)         11 with value (4 36)           1 with value (4 63)
% 0.71/0.90  ;    13 with value (4 13)          5 with value (4 37)           1 with value (4 64)
% 0.71/0.90  ;    15 with value (4 14)          4 with value (4 38)           4 with value (4 65)
% 0.71/0.90  ;    21 with value (4 15)          6 with value (4 39)           2 with value (4 66)
% 0.71/0.90  ;    16 with value (4 16)         18 with value (4 40)           2 with value (4 67)
% 0.71/0.90  ;    22 with value (4 17)          9 with value (4 41)           4 with value (4 68)
% 0.71/0.90  ;    25 with value (4 18)          7 with value (4 42)           1 with value (4 70)
% 0.71/0.90  ;    27 with value (4 19)         15 with value (4 43)           5 with value (4 71)
% 0.71/0.90  ;    29 with value (4 20)          6 with value (4 44)           2 with value (4 78)
% 0.71/0.90  ;    19 with value (4 21)          5 with value (4 45)           3 with value (4 87)
% 0.71/0.90  ;    13 with value (4 22)          6 with value (4 46)           1 with value (4 104)
% 0.71/0.90  ;    21 with value (4 23)          2 with value (4 48)           2 with value (4 106)
% 0.71/0.90  ;    16 with value (4 24)          3 with value (4 49)           1 with value (4 113)
% 0.71/0.90  ;    15 with value (4 25)          2 with value (4 50)           1 with value (4 127)
% 0.71/0.90  ;    11 with value (4 26)          2 with value (4 51)           2 with value (4 129)
% 0.71/0.90  ;    18 with value (4 27)          3 with value (4 52)           2 with value (4 144)
% 0.71/0.90  ;    14 with value (4 28)          2 with value (4 53)
% 0.71/0.90  Evaluation took:
% 0.71/0.90    0.42 seconds of real time
% 0.71/0.90    0.387989 seconds of user run time
% 0.71/0.90    0.031246 seconds of system run time
% 0.71/0.90    [Run times include 0.022 seconds GC run time.]
% 0.71/0.90    0 calls to %EVAL
% 0.71/0.90    0 page faults and
% 0.71/0.90    32,345,936 bytes consed.
% 0.71/0.90  :PROOF-FOUND
% 0.71/0.90  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-07-10T18:35:21
% 0.71/0.90  :PROOF-FOUND
% 0.71/0.90  * 
%------------------------------------------------------------------------------