TSTP Solution File: COL002-4 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n026.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 3.44s 3.64s
% Output   : Refutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;   2 RR)
%            Number of literals    :   12 (  11 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   17 (   0 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,
    weak_fixed_point(X) = apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).

cnf(prove_weak_fixed_point,negated_conjecture,
    weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).

cnf(29,plain,
    apply(apply(apply(s,i),X),Y) = apply(Y,apply(X,Y)),
    inference('PARAMODULATE',[status(thm)],[s_definition,i_definition,theory(equality)]) ).

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

cnf(85,plain,
    apply(apply(apply(s,i),i),X) = apply(X,X),
    inference('PARAMODULATE',[status(thm)],[29,i_definition,theory(equality)]) ).

cnf(87,plain,
    weak_fixed_point(X) = apply(apply(apply(s,i),i),apply(apply(s,apply(b,X)),i)),
    inference('REWRITE',[status(thm)],[weak_fixed_point,85,theory(equality)]) ).

cnf(145,plain,
    apply(apply(apply(s,apply(b,X)),i),Y) = apply(X,apply(Y,Y)),
    inference('PARAMODULATE',[status(thm)],[b_definition,30,theory(equality)]) ).

cnf(776,plain,
    weak_fixed_point(X) = apply(X,weak_fixed_point(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[85,145,theory(equality)]),85,87,theory(equality)]) ).

cnf(777,plain,
    $false,
    inference('REWRITE',[status(thm)],[prove_weak_fixed_point,776,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : COL002-4 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.10/0.12  % Command  : run-snark %s %d
% 0.11/0.33  % Computer : n026.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Tue May 31 08:12:56 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.43  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44  * 
% 0.18/0.44  * 
% 0.18/0.44  #<PACKAGE "SNARK-USER">
% 0.18/0.44  * 
% 0.18/0.44  SNARK-TPTP-OPTIONS
% 0.18/0.44  * 
% 0.18/0.44  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.44   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.44   (USE-FACTORING :POS)
% 0.18/0.44   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.44   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.44   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.44   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.44   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.44   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.44   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.44   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.44   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.44   (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.44  * 
% 0.18/0.44  "."
% 0.18/0.44  * 
% 0.18/0.44  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T08:12:56
% 0.18/0.44  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n026.cluster.edu at 2022-05-31T08:12:56
% 0.18/0.45  
% 3.44/3.64  ; Recognized left identity assertion (= (|apply| |i| ?X) ?X).
% 3.44/3.64  
% 3.44/3.64  #||
% 3.44/3.64  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.64  % SZS output start Refutation
% See solution above
% 3.44/3.64  ||#
% 3.44/3.64  
% 3.44/3.64  ; Summary of computation:
% 3.44/3.64  ;      1498 formulas have been input or derived (from 28 formulas).
% 3.44/3.64  ;       777 (52%) were retained.  Of these,
% 3.44/3.64  ;           23 ( 3%) were simplified or subsumed later,
% 3.44/3.64  ;          754 (97%) are still being kept.
% 3.44/3.64  ; 
% 3.44/3.64  ; Run time in seconds excluding printing time:
% 3.44/3.64  ;     0.002   0%   Read assertion file          (1 call)
% 3.44/3.64  ;     0.000   0%   Assert                       (6 calls)
% 3.44/3.64  ;     0.109   3%   Process new row              (1,492 calls)
% 3.44/3.64  ;     0.000   0%   Resolution                   (54 calls)
% 3.44/3.64  ;     0.026   1%   Paramodulation               (27 calls)
% 3.44/3.64  ;     0.704  22%   Forward simplification       (1,287 calls)
% 3.44/3.64  ;     0.318  10%   Backward simplification      (777 calls)
% 3.44/3.64  ;     2.002  63%   Ordering                     (348,532 calls)
% 3.44/3.64  ;     0.001   0%   Sortal reasoning             (32 calls)
% 3.44/3.64  ;     0.000   0%   Purity testing               (1 call)
% 3.44/3.64  ;     0.027   1%   Other
% 3.44/3.64  ;     3.189        Total
% 3.44/3.64  ;     3.195        Real time
% 3.44/3.64  ; 
% 3.44/3.64  ; Term-hash-array has 3,183 terms in all.
% 3.44/3.64  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 3.44/3.64  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 3.44/3.64  ; Path-index has 3,129 entries (3,132 at peak, 3,203 added, 74 deleted).
% 3.44/3.64  ; Path-index has 779 nodes (785 at peak, 804 added, 25 deleted).
% 3.44/3.64  ; Trie-index has 3,129 entries (3,132 at peak, 3,203 added, 74 deleted).
% 3.44/3.64  ; Trie-index has 15,254 nodes (15,263 at peak, 15,642 added, 388 deleted).
% 3.44/3.64  ; Retrieved 278,020 generalization terms in 15,169 calls.
% 3.44/3.64  ; Retrieved 189,512 instance terms in 2,102 calls.
% 3.44/3.64  ; Retrieved 17,932 unifiable terms in 267 calls.
% 3.44/3.64  ; 
% 3.44/3.64  ; The agenda of rows to process has 6 entries:
% 3.44/3.64  ;     1 with value 40              3 with value 45               2 with value 47
% 3.44/3.64  ; The agenda of rows to give has 731 entries:
% 3.44/3.64  ;     1 with value (4 13)         77 with value (4 31)           8 with value (4 41)
% 3.44/3.64  ;     3 with value (4 22)         75 with value (4 32)          11 with value (4 42)
% 3.44/3.64  ;    10 with value (4 23)         44 with value (4 33)           1 with value (4 43)
% 3.44/3.64  ;    18 with value (4 24)         27 with value (4 34)           7 with value (4 44)
% 3.44/3.64  ;    37 with value (4 25)         25 with value (4 35)           1 with value (4 45)
% 3.44/3.64  ;    52 with value (4 26)         17 with value (4 36)           1 with value (4 47)
% 3.44/3.64  ;    56 with value (4 27)         14 with value (4 37)           4 with value (4 49)
% 3.44/3.64  ;    57 with value (4 28)         26 with value (4 38)           1 with value (4 50)
% 3.44/3.64  ;    59 with value (4 29)         14 with value (4 39)           1 with value (4 53)
% 3.44/3.64  ;    73 with value (4 30)         11 with value (4 40)
% 3.44/3.64  Evaluation took:
% 3.44/3.64    3.195 seconds of real time
% 3.44/3.64    2.753725 seconds of user run time
% 3.44/3.64    0.43708 seconds of system run time
% 3.44/3.64    [Run times include 0.098 seconds GC run time.]
% 3.44/3.64    0 calls to %EVAL
% 3.44/3.64    0 page faults and
% 3.44/3.64    242,306,920 bytes consed.
% 3.44/3.64  :PROOF-FOUND
% 3.44/3.64  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-05-31T08:12:59
% 3.44/3.64  :PROOF-FOUND
% 3.44/3.64  * 
%------------------------------------------------------------------------------