TSTP Solution File: COL002-2 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : COL002-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n022.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 : Fri Jul 15 00:41:33 EDT 2022

% Result   : Unsatisfiable 1.45s 1.63s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   9 unt;   0 nHn;   5 RR)
%            Number of literals    :   13 (   8 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   17 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
    apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).

cnf(b_definition,axiom,
    apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).

cnf(i_definition,axiom,
    apply(i,X) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).

cnf(weak_fixed_point,axiom,
    ( X != apply(fixed_pt,X)
    | fixed_point(X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).

cnf(prove_weak_fixed_point,negated_conjecture,
    ~ fixed_point(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).

cnf(9,plain,
    ( apply(X,Y) != apply(apply(apply(b,fixed_pt),X),Y)
    | fixed_point(apply(X,Y)) ),
    inference('PARAMODULATE',[status(thm)],[weak_fixed_point,b_definition,theory(equality)]) ).

cnf(30,plain,
    apply(apply(apply(s,i),X),Y) = apply(Y,apply(X,Y)),
    inference('PARAMODULATE',[status(thm)],[s_definition,i_definition,theory(equality)]) ).

cnf(31,plain,
    apply(apply(apply(s,X),i),Y) = apply(apply(X,Y),Y),
    inference('PARAMODULATE',[status(thm)],[s_definition,i_definition,theory(equality)]) ).

cnf(83,plain,
    apply(apply(apply(s,i),i),X) = apply(X,X),
    inference('PARAMODULATE',[status(thm)],[30,i_definition,theory(equality)]) ).

cnf(85,plain,
    ~ fixed_point(apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i))),
    inference('REWRITE',[status(thm)],[prove_weak_fixed_point,83,theory(equality)]) ).

cnf(436,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[9,31]),85,83,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COL002-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue May 31 06:19:52 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47  * 
% 0.19/0.47  * 
% 0.19/0.48  #<PACKAGE "SNARK-USER">
% 0.19/0.48  * 
% 0.19/0.48  SNARK-TPTP-OPTIONS
% 0.19/0.48  * 
% 0.19/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.48   (USE-FACTORING :POS)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.48  * 
% 0.19/0.48  "."
% 0.19/0.48  * 
% 0.19/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T06:19:52
% 0.19/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n022.cluster.edu at 2022-05-31T06:19:52
% 0.19/0.49  
% 1.45/1.63  ; Recognized left identity assertion (= (|apply| |i| ?X) ?X).
% 1.45/1.63  
% 1.45/1.63  #||
% 1.45/1.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.45/1.63  % SZS output start Refutation
% See solution above
% 1.45/1.63  ||#
% 1.45/1.63  
% 1.45/1.63  ; Summary of computation:
% 1.45/1.63  ;       845 formulas have been input or derived (from 23 formulas).
% 1.45/1.63  ;       436 (52%) were retained.  Of these,
% 1.45/1.63  ;           11 ( 3%) were simplified or subsumed later,
% 1.45/1.63  ;          425 (97%) are still being kept.
% 1.45/1.63  ; 
% 1.45/1.63  ; Run time in seconds excluding printing time:
% 1.45/1.63  ;     0.002   0%   Read assertion file          (1 call)
% 1.45/1.63  ;     0.000   0%   Assert                       (6 calls)
% 1.45/1.63  ;     0.040   3%   Process new row              (799 calls)
% 1.45/1.63  ;     0.001   0%   Resolution                   (44 calls)
% 1.45/1.63  ;     0.016   1%   Paramodulation               (22 calls)
% 1.45/1.63  ;     0.000   0%   Condensing                   (11 calls)
% 1.45/1.63  ;     0.000   0%   Forward subsumption          (11 calls)
% 1.45/1.63  ;     0.000   0%   Backward subsumption         (3 calls)
% 1.45/1.63  ;     0.001   0%   Clause clause subsumption    (8 calls)
% 1.45/1.63  ;     0.210  18%   Forward simplification       (709 calls)
% 1.45/1.63  ;     0.141  12%   Backward simplification      (436 calls)
% 1.45/1.63  ;     0.716  62%   Ordering                     (124,470 calls)
% 1.45/1.63  ;     0.000   0%   Sortal reasoning             (32 calls)
% 1.45/1.63  ;     0.000   0%   Purity testing               (1 call)
% 1.45/1.63  ;     0.024   2%   Other
% 1.45/1.63  ;     1.151        Total
% 1.45/1.63  ;     1.153        Real time
% 1.45/1.63  ; 
% 1.45/1.63  ; Term-hash-array has 1,865 terms in all.
% 1.45/1.63  ; Feature-vector-row-index has 3 entries (3 at peak, 3 added, 0 deleted).
% 1.45/1.63  ; Feature-vector-row-index has 24 nodes (24 at peak, 24 added, 0 deleted).
% 1.45/1.63  ;  Retrieved 8 possibly forward subsuming rows in 11 calls.
% 1.45/1.63  ;  Retrieved 0 possibly backward subsumed rows in 3 calls.
% 1.45/1.63  ; Path-index has 1,843 entries (1,843 at peak, 1,877 added, 34 deleted).
% 1.45/1.63  ; Path-index has 663 nodes (663 at peak, 698 added, 35 deleted).
% 1.45/1.63  ; Trie-index has 1,843 entries (1,843 at peak, 1,877 added, 34 deleted).
% 1.45/1.63  ; Trie-index has 8,092 nodes (8,092 at peak, 8,290 added, 198 deleted).
% 1.45/1.63  ; Retrieved 83,131 generalization terms in 7,190 calls.
% 1.45/1.63  ; Retrieved 70,324 instance terms in 1,164 calls.
% 1.45/1.63  ; Retrieved 8,505 unifiable terms in 208 calls.
% 1.45/1.63  ; 
% 1.45/1.63  ; The agenda of rows to process has 44 entries:
% 1.45/1.63  ;     1 with value 24              2 with value 32               4 with value 37
% 1.45/1.63  ;     4 with value 26              4 with value 33               3 with value 38
% 1.45/1.63  ;     4 with value 28              4 with value 34               3 with value 41
% 1.45/1.63  ;     2 with value 29              5 with value 35               1 with value 43
% 1.45/1.63  ;     2 with value 31              5 with value 36
% 1.45/1.63  ; The agenda of rows to give has 405 entries:
% 1.45/1.63  ;    10 with value (4 22)         46 with value (4 30)           4 with value (4 38)
% 1.45/1.63  ;     9 with value (4 23)         50 with value (4 31)           4 with value (4 39)
% 1.45/1.63  ;    18 with value (4 24)         21 with value (4 32)           2 with value (4 40)
% 1.45/1.63  ;    30 with value (4 25)         14 with value (4 33)           1 with value (4 41)
% 1.45/1.63  ;    51 with value (4 26)          7 with value (4 34)           1 with value (4 42)
% 1.45/1.63  ;    32 with value (4 27)          5 with value (4 35)           1 with value (4 44)
% 1.45/1.63  ;    50 with value (4 28)          5 with value (4 36)           1 with value (4 49)
% 1.45/1.63  ;    39 with value (4 29)          4 with value (4 37)
% 1.45/1.63  Evaluation took:
% 1.45/1.63    1.153 seconds of real time
% 1.45/1.63    1.00999 seconds of user run time
% 1.45/1.63    0.142738 seconds of system run time
% 1.45/1.63    [Run times include 0.03 seconds GC run time.]
% 1.45/1.63    0 calls to %EVAL
% 1.45/1.63    0 page faults and
% 1.45/1.63    82,357,816 bytes consed.
% 1.45/1.63  :PROOF-FOUND
% 1.45/1.63  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T06:19:54
% 1.45/1.63  :PROOF-FOUND
% 1.45/1.63  * 
%------------------------------------------------------------------------------