TSTP Solution File: GRP169-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n018.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 : Sat Jul 16 11:37:15 EDT 2022

% Result   : Unsatisfiable 0.84s 0.99s
% Output   : Refutation 0.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  19 unt;   0 nHn;   4 RR)
%            Number of literals    :   19 (  18 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;   3 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).

cnf(p02a_1,hypothesis,
    least_upper_bound(inverse(a),inverse(b)) = inverse(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p02a_1) ).

cnf(prove_p02a,negated_conjecture,
    least_upper_bound(a,b) != a,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p02a) ).

cnf(68,plain,
    X = multiply(inverse(Y),multiply(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(69,plain,
    multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
    inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).

cnf(89,plain,
    multiply(inverse(b),X) = least_upper_bound(multiply(inverse(a),X),multiply(inverse(b),X)),
    inference('PARAMODULATE',[status(thm)],[monotony_lub2,p02a_1,theory(equality)]) ).

cnf(110,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[68,left_inverse,theory(equality)]) ).

cnf(111,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[68,68,theory(equality)]) ).

cnf(112,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[110,111,theory(equality)]) ).

cnf(113,plain,
    multiply(multiply(X,inverse(Y)),Y) = X,
    inference('REWRITE',[status(thm)],[69,112,theory(equality)]) ).

cnf(121,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[113,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(129,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[68,121,theory(equality)]) ).

cnf(286,plain,
    identity = least_upper_bound(multiply(inverse(a),b),identity),
    inference('PARAMODULATE',[status(thm)],[89,left_inverse,theory(equality)]) ).

cnf(308,plain,
    X = least_upper_bound(multiply(X,multiply(inverse(a),b)),X),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[monotony_lub1,286,theory(equality)]),112,theory(equality)]) ).

cnf(392,plain,
    $false,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[308,129,theory(equality)]),prove_p02a]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GRP169-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14  % Command  : run-snark %s %d
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Mon Jun 13 15:34:57 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.22/0.48  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.49  * 
% 0.22/0.49  * 
% 0.22/0.50  #<PACKAGE "SNARK-USER">
% 0.22/0.50  * 
% 0.22/0.50  SNARK-TPTP-OPTIONS
% 0.22/0.50  * 
% 0.22/0.50  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.50   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.50   (USE-FACTORING :POS)
% 0.22/0.50   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.50   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.50   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.50   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.50   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.50   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.50   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.50   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.50   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.50   (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.50  * 
% 0.22/0.50  "."
% 0.22/0.50  * 
% 0.22/0.50  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T15:34:58
% 0.22/0.50  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-13T15:34:58
% 0.22/0.52  
% 0.22/0.52  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.22/0.52  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.22/0.52  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.22/0.52  ; Recognized commutativity assertion (= (|greatest_lower_bound| ?X ?Y) (|greatest_lower_bound| ?Y ?X)).
% 0.22/0.52  ; Recognized commutativity assertion (= (|least_upper_bound| ?X ?Y) (|least_upper_bound| ?Y ?X)).
% 0.22/0.52  ; Recognized associativity assertion (= (|greatest_lower_bound| ?X (|greatest_lower_bound| ?Y ?Z)) (|greatest_lower_bound| (|greatest_lower_bound| ?X ?Y) ?Z)).
% 0.22/0.52  ; Recognized associativity assertion (= (|least_upper_bound| ?X (|least_upper_bound| ?Y ?Z)) (|least_upper_bound| (|least_upper_bound| ?X ?Y) ?Z)).
% 0.22/0.52  ; Declaring greatest_lower_bound to be commutative.
% 0.22/0.52  ; Declaring greatest_lower_bound to be associative-commutative.
% 0.22/0.52  ; Declaring least_upper_bound to be commutative.
% 0.84/0.99  ; Declaring least_upper_bound to be associative-commutative.
% 0.84/0.99  
% 0.84/0.99  #||
% 0.84/0.99  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.84/0.99  % SZS output start Refutation
% See solution above
% 0.84/0.99  ||#
% 0.84/0.99  
% 0.84/0.99  ; Summary of computation:
% 0.84/0.99  ;      2212 formulas have been input or derived (from 56 formulas).
% 0.84/0.99  ;       392 (18%) were retained.  Of these,
% 0.84/0.99  ;           34 ( 9%) were simplified or subsumed later,
% 0.84/0.99  ;          358 (91%) are still being kept.
% 0.84/0.99  ; 
% 0.84/0.99  ; Run time in seconds excluding printing time:
% 0.84/0.99  ;     0.004   1%   Read assertion file          (1 call)
% 0.84/0.99  ;     0.001   0%   Assert                       (17 calls)
% 0.84/0.99  ;     0.045   9%   Process new row              (2,121 calls)
% 0.84/0.99  ;     0.004   1%   Resolution                   (110 calls)
% 0.84/0.99  ;     0.047  10%   Paramodulation               (55 calls)
% 0.84/0.99  ;     0.007   1%   Embedding                    (175 calls)
% 0.84/0.99  ;     0.308  63%   Forward simplification       (1,890 calls)
% 0.84/0.99  ;     0.010   2%   Backward simplification      (221 calls)
% 0.84/0.99  ;     0.026   5%   Ordering                     (6,873 calls)
% 0.84/0.99  ;     0.005   1%   Ordering ac                  (644 calls)
% 0.84/0.99  ;     0.000   0%   Sortal reasoning             (32 calls)
% 0.84/0.99  ;     0.000   0%   Purity testing               (1 call)
% 0.84/0.99  ;     0.033   7%   Other
% 0.84/0.99  ;     0.490        Total
% 0.84/0.99  ;     0.491        Real time
% 0.84/0.99  ; 
% 0.84/0.99  ; Term-hash-array has 1,174 terms in all.
% 0.84/0.99  ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.84/0.99  ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.84/0.99  ; Path-index has 1,093 entries (1,093 at peak, 1,185 added, 92 deleted).
% 0.84/0.99  ; Path-index has 859 nodes (859 at peak, 877 added, 18 deleted).
% 0.84/0.99  ; Trie-index has 1,093 entries (1,093 at peak, 1,185 added, 92 deleted).
% 0.84/0.99  ; Trie-index has 629 nodes (629 at peak, 749 added, 120 deleted).
% 0.84/0.99  ; Retrieved 377,590 generalization terms in 22,101 calls.
% 0.84/0.99  ; Retrieved 557 instance terms in 255 calls.
% 0.84/0.99  ; Retrieved 5,642 unifiable terms in 329 calls.
% 0.84/0.99  ; 
% 0.84/0.99  ; The agenda of rows to process has 47 entries:
% 0.84/0.99  ;     1 with value 14              6 with value 26               3 with value 35
% 0.84/0.99  ;     1 with value 15              2 with value 27               1 with value 36
% 0.84/0.99  ;     2 with value 16              1 with value 28               1 with value 37
% 0.84/0.99  ;     1 with value 17              1 with value 29               2 with value 39
% 0.84/0.99  ;     1 with value 18              2 with value 30               1 with value 40
% 0.84/0.99  ;     1 with value 19              2 with value 31               2 with value 41
% 0.84/0.99  ;     1 with value 22              6 with value 33               1 with value 44
% 0.84/0.99  ;     1 with value 23              4 with value 34               1 with value 45
% 0.84/0.99  ;     2 with value 24
% 0.84/0.99  ; The agenda of rows to give has 305 entries:
% 0.84/0.99  ;     3 with value (4 18)         24 with value (4 25)          18 with value (4 31)
% 0.84/0.99  ;     3 with value (4 19)         25 with value (4 26)          10 with value (4 33)
% 0.84/0.99  ;    30 with value (4 20)         50 with value (4 27)           4 with value (4 34)
% 0.84/0.99  ;    14 with value (4 21)         16 with value (4 28)           6 with value (4 36)
% 0.84/0.99  ;    19 with value (4 22)         22 with value (4 29)           2 with value (4 39)
% 0.84/0.99  ;    19 with value (4 23)         10 with value (4 30)           2 with value (4 42)
% 0.84/0.99  ;    28 with value (4 24)
% 0.84/0.99  Evaluation took:
% 0.84/0.99    0.491 seconds of real time
% 0.84/0.99    0.465089 seconds of user run time
% 0.84/0.99    0.026684 seconds of system run time
% 0.84/0.99    [Run times include 0.01 seconds GC run time.]
% 0.84/0.99    0 calls to %EVAL
% 0.84/0.99    0 page faults and
% 0.84/0.99    27,267,688 bytes consed.
% 0.84/0.99  :PROOF-FOUND
% 0.84/0.99  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T15:34:58
% 0.84/0.99  :PROOF-FOUND
% 0.84/0.99  * 
%------------------------------------------------------------------------------