TSTP Solution File: SET018-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n003.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 05:05:52 EDT 2022

% Result   : Unsatisfiable 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   36 (  22 unt;  13 nHn;  30 RR)
%            Number of literals    :   52 (  32 equ;   8 neg)
%            Maximal clause size   :    3 (   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;   4 con; 0-2 aty)
%            Number of variables   :   19 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(singleton_1,axiom,
    member(X,singleton_set(X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_1) ).

cnf(singleton_2,axiom,
    ( ~ member(X,singleton_set(Y))
    | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_2) ).

cnf(unordered_pair_1,axiom,
    member(X,unordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_1) ).

cnf(unordered_pair_2,axiom,
    member(X,unordered_pair(Y,X)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_2) ).

cnf(unordered_pair_3,axiom,
    ( ~ member(X,unordered_pair(Y,Z))
    | X = Y
    | X = Z ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_3) ).

cnf(ordered_pair,axiom,
    ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

cnf(equal_ordered_pairs,hypothesis,
    ordered_pair(m1,r1) = ordered_pair(m2,r2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).

cnf(prove_second_components_equal,negated_conjecture,
    r1 != r2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).

cnf(9,plain,
    ~ member(r1,singleton_set(r2)),
    inference('UR-RESOLVE',[status(thm)],[singleton_2,prove_second_components_equal]) ).

cnf(11,plain,
    member(singleton_set(X),ordered_pair(X,Y)),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_1,ordered_pair,theory(equality)]) ).

cnf(12,plain,
    member(unordered_pair(X,Y),ordered_pair(X,Y)),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_2,ordered_pair,theory(equality)]) ).

cnf(14,plain,
    ~ member(r1,unordered_pair(r2,r2)),
    inference('UR-RESOLVE',[status(thm)],[unordered_pair_3,prove_second_components_equal,prove_second_components_equal]) ).

cnf(16,plain,
    ( ~ member(X,ordered_pair(Y,Z))
    | X = singleton_set(Y)
    | X = unordered_pair(Y,Z) ),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_3,ordered_pair,theory(equality)]) ).

cnf(17,plain,
    member(singleton_set(m2),ordered_pair(m1,r1)),
    inference('PARAMODULATE',[status(thm)],[11,equal_ordered_pairs,theory(equality)]) ).

cnf(18,plain,
    member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
    inference('PARAMODULATE',[status(thm)],[12,equal_ordered_pairs,theory(equality)]) ).

cnf(28,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | singleton_set(m2) = unordered_pair(m1,r1) ),
    inference('HYPERRESOLVE',[status(thm)],[16,17]) ).

cnf(29,plain,
    ( unordered_pair(m2,r2) = singleton_set(m1)
    | unordered_pair(m2,r2) = unordered_pair(m1,r1) ),
    inference('HYPERRESOLVE',[status(thm)],[16,18]) ).

cnf(31,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | member(m1,singleton_set(m2)) ),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_1,28,theory(equality)]) ).

cnf(36,plain,
    ( singleton_set(m2) = singleton_set(m1)
    | m1 = m2 ),
    inference('HYPERRESOLVE',[status(thm)],[singleton_2,31]) ).

cnf(37,plain,
    ( m1 = m2
    | member(m2,singleton_set(m1)) ),
    inference('PARAMODULATE',[status(thm)],[singleton_1,36,theory(equality)]) ).

cnf(45,plain,
    m1 = m2,
    inference('HYPERRESOLVE',[status(thm)],[singleton_2,37]) ).

cnf(46,plain,
    ordered_pair(m1,r1) = ordered_pair(m1,r2),
    inference('REWRITE',[status(thm)],[equal_ordered_pairs,45,theory(equality)]) ).

cnf(50,plain,
    ( unordered_pair(m1,r2) = singleton_set(m1)
    | unordered_pair(m1,r2) = unordered_pair(m1,r1) ),
    inference('REWRITE',[status(thm)],[29,45,theory(equality)]) ).

cnf(52,plain,
    ( unordered_pair(m1,r2) = singleton_set(m1)
    | member(r2,unordered_pair(m1,r1)) ),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_2,50,theory(equality)]) ).

cnf(54,plain,
    ( unordered_pair(m1,r2) = singleton_set(m1)
    | r2 = m1 ),
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[unordered_pair_3,52]),prove_second_components_equal]) ).

cnf(55,plain,
    ( r2 = m1
    | member(r2,singleton_set(m1)) ),
    inference('PARAMODULATE',[status(thm)],[unordered_pair_2,54,theory(equality)]) ).

cnf(59,plain,
    r2 = m1,
    inference('HYPERRESOLVE',[status(thm)],[singleton_2,55]) ).

cnf(61,plain,
    ~ member(r1,singleton_set(m1)),
    inference('REWRITE',[status(thm)],[9,59,theory(equality)]) ).

cnf(63,plain,
    ~ member(r1,unordered_pair(m1,m1)),
    inference('REWRITE',[status(thm)],[14,59,theory(equality)]) ).

cnf(65,plain,
    ordered_pair(m1,r1) = ordered_pair(m1,m1),
    inference('REWRITE',[status(thm)],[46,59,theory(equality)]) ).

cnf(67,plain,
    ( unordered_pair(m1,m1) = singleton_set(m1)
    | unordered_pair(m1,m1) = unordered_pair(m1,r1) ),
    inference('REWRITE',[status(thm)],[50,59,theory(equality)]) ).

cnf(69,plain,
    member(unordered_pair(m1,r1),ordered_pair(m1,m1)),
    inference('PARAMODULATE',[status(thm)],[12,65,theory(equality)]) ).

cnf(71,plain,
    ( unordered_pair(m1,r1) = singleton_set(m1)
    | unordered_pair(m1,m1) = unordered_pair(m1,r1) ),
    inference('HYPERRESOLVE',[status(thm)],[16,69]) ).

cnf(72,plain,
    unordered_pair(m1,m1) = singleton_set(m1),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[unordered_pair_2,67,theory(equality)]),63]) ).

cnf(74,plain,
    unordered_pair(m1,r1) = singleton_set(m1),
    inference('REWRITE',[status(thm)],[71,72,theory(equality)]) ).

cnf(76,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[unordered_pair_2,74,theory(equality)]),61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : run-snark %s %d
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 08:14:15 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.44  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45  * 
% 0.20/0.45  * 
% 0.20/0.46  #<PACKAGE "SNARK-USER">
% 0.20/0.46  * 
% 0.20/0.46  SNARK-TPTP-OPTIONS
% 0.20/0.46  * 
% 0.20/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46   (USE-FACTORING :POS)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.46  * 
% 0.20/0.46  "."
% 0.20/0.46  * 
% 0.20/0.46  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T08:14:15
% 0.20/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n003.cluster.edu at 2022-07-11T08:14:15
% 0.20/0.51  
% 0.20/0.51  
% 0.20/0.51  #||
% 0.20/0.51  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51  % SZS output start Refutation
% See solution above
% 0.20/0.51  ||#
% 0.20/0.51  
% 0.20/0.51  ; Summary of computation:
% 0.20/0.51  ;       203 formulas have been input or derived (from 45 formulas).
% 0.20/0.51  ;        76 (37%) were retained.  Of these,
% 0.20/0.51  ;           51 (67%) were simplified or subsumed later,
% 0.20/0.51  ;           25 (33%) are still being kept.
% 0.20/0.51  ; 
% 0.20/0.51  ; Run time in seconds excluding printing time:
% 0.20/0.51  ;     0.001   2%   Read assertion file          (1 call)
% 0.20/0.51  ;     0.000   0%   Assert                       (8 calls)
% 0.20/0.51  ;     0.008  16%   Process new row              (196 calls)
% 0.20/0.51  ;     0.003   6%   Resolution                   (88 calls)
% 0.20/0.51  ;     0.002   4%   Paramodulation               (44 calls)
% 0.20/0.51  ;     0.000   0%   Factoring                    (9 calls)
% 0.20/0.51  ;     0.002   4%   Condensing                   (43 calls)
% 0.20/0.51  ;     0.002   4%   Forward subsumption          (43 calls)
% 0.20/0.51  ;     0.001   2%   Backward subsumption         (36 calls)
% 0.20/0.51  ;     0.000   0%   Clause clause subsumption    (17 calls)
% 0.20/0.51  ;     0.003   6%   Forward simplification       (189 calls)
% 0.20/0.51  ;     0.002   4%   Backward simplification      (76 calls)
% 0.20/0.51  ;     0.002   4%   Ordering                     (203 calls)
% 0.20/0.51  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.20/0.51  ;     0.000   0%   Purity testing               (1 call)
% 0.20/0.51  ;     0.024  48%   Other
% 0.20/0.51  ;     0.050        Total
% 0.20/0.51  ;     0.055        Real time
% 0.20/0.51  ; 
% 0.20/0.51  ; Term-hash-array has 138 terms in all.
% 0.20/0.51  ; Feature-vector-row-index has 5 entries (22 at peak, 36 added, 31 deleted).
% 0.20/0.51  ; Feature-vector-row-index has 25 nodes (224 at peak, 373 added, 348 deleted).
% 0.20/0.51  ;  Retrieved 18 possibly forward subsuming rows in 43 calls.
% 0.20/0.51  ;  Retrieved 0 possibly backward subsumed rows in 36 calls.
% 0.20/0.51  ; Path-index has 58 entries (105 at peak, 164 added, 106 deleted).
% 0.20/0.51  ; Path-index has 193 nodes (272 at peak, 362 added, 169 deleted).
% 0.20/0.51  ; Trie-index has 58 entries (105 at peak, 164 added, 106 deleted).
% 0.20/0.51  ; Trie-index has 183 nodes (364 at peak, 541 added, 358 deleted).
% 0.20/0.51  ; Retrieved 171 generalization terms in 613 calls.
% 0.20/0.51  ; Retrieved 40 instance terms in 39 calls.
% 0.20/0.51  ; Retrieved 255 unifiable terms in 306 calls.
% 0.20/0.51  ; 
% 0.20/0.51  ; The agenda of rows to process has 5 entries:
% 0.20/0.51  ;     1 with value 11              2 with value 16               1 with value 18
% 0.20/0.51  ;     1 with value 12
% 0.20/0.51  ; The agenda of rows to give has 5 entries:
% 0.20/0.51  ;     1 with value (4 12)          1 with value (4 21)           1 with value (4 28)
% 0.20/0.51  ;     1 with value (4 15)          1 with value (4 27)
% 0.20/0.51  Evaluation took:
% 0.20/0.51    0.055 seconds of real time
% 0.20/0.51    0.047916 seconds of user run time
% 0.20/0.51    0.007104 seconds of system run time
% 0.20/0.51    0 calls to %EVAL
% 0.20/0.51    0 page faults and
% 0.20/0.51    4,741,392 bytes consed.
% 0.20/0.51  :PROOF-FOUND
% 0.20/0.51  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-07-11T08:14:15
% 0.20/0.51  :PROOF-FOUND
% 0.20/0.51  * 
%------------------------------------------------------------------------------